AMG FUNDS III

Filed pursuant to Rule 497(e)

File Nos. 002‑84012 and 811‑03752

AMG FUNDS III

AMG GW&K ESG Bond Fund

Supplement dated September 11, 2026 to the Prospectus and Statement of Additional Information, each dated May 1, 2026

The following information supplements and supersedes any information to the contrary relating to AMG GW&K ESG Bond Fund (the “Fund”), a series of AMG Funds III, contained in the Fund’s Prospectus (the “Prospectus”) and Statement of Additional Information (the “SAI”), dated as noted above.

Effective immediately, the Fund’s name is changed from AMG GW&K ESG Bond Fund to AMG GW&K Enhanced Core Bond Fund. All references to AMG GW&K ESG Bond Fund in the Prospectus and SAI are deleted and replaced with “AMG GW&K Enhanced Core Bond Fund.”

In addition, effective immediately, the Prospectus is revised as follows:

The following paragraph is added as the last paragraph of the section titled “Summary of the Funds – AMG GW&K ESG Bond Fund – Principal Investment Strategies” beginning on page 3 and as the penultimate paragraph of the section titled “Additional Information About the Funds – AMG GW&K ESG Bond Fund – Additional Information About the Fund’s Principal Investment Strategies” on page 12:

The Fund may use derivatives and similar instruments for a variety of purposes, including hedging, risk management, portfolio management or to earn income. The Fund’s use of derivatives may involve the purchase and sale of derivative instruments such as futures, options, to‑be‑announced (TBA) commitments, swaps and other similar instruments and techniques. The Fund’s investments in derivative instruments and other investments that provide investment exposure to the investments suggested by the Fund’s name, or that provide investment exposure to one or more market risk factors associated with the investment focus that the Fund’s name suggests, may be counted toward the Fund’s 80% investment policy.

The section titled “Summary of the Funds – AMG GW&K ESG Bond Fund – Principal Risks” beginning on page 4 is revised to add the following as principal risks of the Fund:

Derivatives Risk—the use of derivatives involves costs, the risk that the value of derivatives may not correlate perfectly with their underlying assets, rates or indices, liquidity risk, and the risk of mispricing or improper valuation. The use of derivatives may not succeed for various reasons, and the complexity and rapidly changing structure of derivatives markets may increase the possibility of market losses.

Leverage Risk—borrowing and some derivative investments such as futures, forward commitment transactions and swaps may increase volatility and magnify smaller adverse market movements into relatively larger losses.

Also with respect to the section titled “Summary of the Funds – AMG GW&K ESG Bond Fund – Principal Risks” beginning on page 4, “Credit Risk” is deleted and replaced with the following:

Credit and Counterparty Risk—the issuer of bonds or other debt securities or a counterparty to a derivatives contract (including over‑the‑counter counterparties as well as brokers and clearinghouses in respect of exchange-traded and/or cleared products) may be unable or unwilling, or may be perceived as unable or unwilling, to make timely interest, principal or settlement payments or otherwise honor its obligations. Changes in an issuer’s financial strength, credit rating or the market’s perception of an issuer’s creditworthiness may also affect the value of the Fund’s investment in that issuer.

The third paragraph of the section titled “Summary of the Funds – AMG GW&K ESG Bond Fund – Performance” on page 6 is deleted and replaced with the following:

As of March 19, 2021, GW&K was appointed as subadviser to the Fund and the Fund changed its name to “AMG GW&K ESG Bond Fund,” made changes to its principal investment strategies, and began comparing its performance to the Bloomberg U.S. Aggregate Bond Index. As of September 11, 2026, the Fund changed its name from “AMG GW&K ESG Bond Fund” to “AMG GW&K Enhanced Core Bond Fund” and adopted the Fund’s current investment strategies. The Fund’s past performance would have been different if the Fund were managed using the current investment strategies.

The section titled “Additional Information About the Funds – Summary of the Funds’ Principal Risks” beginning on page 16 is revised to add the following as principal risks of the Fund:

DERIVATIVES RISK

(AMG GW&K Enhanced Core Bond Fund)

Derivatives, including options, futures, forwards and swaps, are financial contracts whose value depends on, or is derived from, the value of an underlying asset, interest rate or index. The use of derivatives will involve costs, the risk that the value of derivatives may not correlate perfectly with their underlying assets, rates, or indices, liquidity risk, the risk of mispricing or improper valuation, and may result in losses or have the effect of accelerating the recognition of gain. Derivative transactions typically involve leverage and may be highly volatile. The use of derivatives may not succeed for various reasons, including unexpected changes in the value of the derivatives or the assets, rates or indices underlying them. Derivatives are also subject to credit and counterparty risk in that a counterparty (including over‑the‑counter counterparties as well as brokers and clearinghouses in respect of exchange-traded and/or cleared products) may fail to honor its obligations and/or become bankrupt or insolvent, causing a loss for the Fund. Government regulation of derivative instruments may limit or prevent the Fund from using such instruments as part of its investment strategies or result in materially increased costs in using such instruments, which could adversely affect the Fund.

LEVERAGE RISK

(AMG GW&K Enhanced Core Bond Fund)

Borrowing, and some derivative investments such as futures, forward commitment transactions and swaps, may create investment leverage. Leverage generally magnifies smaller adverse market movements into relatively larger losses for the Fund. There is no assurance that the Fund will leverage its portfolio, or if it does, that the leveraging strategy will be successful. Leverage may cause the Fund to be more volatile and riskier and magnify the Fund’s losses to an extent greater than if it had not been leveraged.

Also with respect to the section titled “Additional Information About the Funds – Summary of the Funds’ Principal Risks” beginning on page 16, “Credit Risk” is deleted and replaced with the following:

CREDIT AND COUNTERPARTY RISK

(AMG GW&K Enhanced Core Bond Fund)

An issuer of bonds or other debt securities or a counterparty to a derivatives contract (including over‑the‑counter counterparties as well as brokers and clearinghouses in respect of exchange-traded and/or cleared products) may be unable or unwilling, or may be perceived (whether by market participants, ratings agencies, pricing services or otherwise) as unable or unwilling, to make timely interest, principal or settlement payments or otherwise honor its obligations. To the extent the Fund has significant exposure to a counterparty under a derivatives contract (or multiple derivatives contracts), this risk may be particularly pronounced for the Fund. This risk of default for most debt securities is monitored by several nationally recognized statistical rating organizations such as Moody’s and S&P. Actual or perceived changes in a company’s financial health will affect the valuation of its debt securities. Bonds or debt securities rated BBB/Baa by S&P/Moody’s, although investment grade, may have speculative characteristics because their issuers are more vulnerable to financial setbacks and economic pressures than issuers with higher ratings. Changes in an issuer’s financial strength, credit rating or the market’s perception of an issuer’s creditworthiness may also affect the value of the Fund’s investment in that issuer.

In addition, effective immediately, the SAI is revised as follows:

In the “Investment Policies” section, the sub‑section titled “(31) When-Issued, Delayed-Delivery and Forward Commitment Transactions” beginning on page 58 is renamed “(31) When-Issued, Delayed Delivery, Forward Commitment and To‑Be‑Announced Securities” and the following is added at the end of the sub‑section:

AMG GW&K Enhanced Core Bond Fund may purchase or sell securities, including mortgage-backed securities, in the to‑be‑announced (“TBA”) market. A TBA purchase commitment is a security that is purchased or sold for a fixed price and the underlying securities are announced at a future date. The seller does not specify the particular securities to be delivered. Instead, the Fund agrees to accept any security that meets specified terms. For example, in a TBA mortgage-backed security transaction, the Fund and the seller would agree upon the issuer, interest rate and terms of the underlying mortgages. The seller would not identify the specific underlying mortgages until it issues the security. The purchaser of TBA securities may be less favorable than anticipated by the purchaser.

Financial Industry Regulatory Authority (“FINRA”) rules include mandatory margin requirements for the TBA market that require the Fund to post collateral in connection with its TBA transactions. Although FINRA does not impose a requirement on the Fund’s TBA counterparties to also post margin, margin is typically contractually required to be bilaterally exchanged. The required collateralization of TBA trades could increase the cost of TBA transactions to the Fund and impose added operational complexity.

PLEASE KEEP THIS SUPPLEMENT FOR FUTURE REFERENCE