Table of Contents

FORM 6-K

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Report of Foreign Private Issuer

Pursuant to Rule 13a-16 or 15d-16

of the Securities Exchange Act of 1934

For the month of July, 2013

Commission File Number: 001-09531

Telefónica, S.A.

(Translation of registrant’s name into English)

Distrito Telefónica, Ronda de la Comunicación s/n,

28050 Madrid, Spain

3491-482 87 00

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F:

Form 20-F  x            Form 40-F  ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1):

Yes  ¨            No  x

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7):

Yes  ¨             No  x

Indicate by check mark whether by furnishing the information contained in this Form, the registrant is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934:

Yes  ¨            No  x

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): N/A

Table of Contents

Telefónica, S.A.

TABLE OF CONTENTS

Table of Contents

RAMIRO SÁNCHEZ DE LERÍN GARCÍA-OVIES

General Secretary and

Secretary to the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA, S.A. as provided in article 82 of the Spanish Securities Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

Following the Significant Event published on April 30, 2013, related to the agreement reached between Telefónica, S.A. (hereinafter, Telefónica) and Corporación Multi Inversiones (“CMI”), for the sale of the 40% of Telefónica´s stake in Guatemala, El Salvador, Nicaragua and Panama, Telefónica informs that the conditions to which the transaction was subject have been met.

In this regard, it is expected that in accordance with the provisions of the aforementioned agreement, the transaction will be completed in the coming days.

Madrid, July 19, 2013

Table of Contents

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.