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 January, 2016

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

Telefónica, S.A.

TABLE OF CONTENTS

RAMIRO SÁNCHEZ DE LERÍN GARCÍA-OVIES

General Secretary and

Secretary to the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA S.A., pursuant to article 228 of the Spanish Securities Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

On the date hereof, January 12, 2016, DTS, Distribuidora de Television Digital, S.A.U. (“DTS”) and Mediaproducción, S.L.U. (“Mediapro”) have reached an agreement for the broadcasting of the thematic pay TV channel called “BeIN Sports LaLiga” with contents of the Spanish National League Championship First and Second Division and the Copa del S.M. el Rey, corresponding to the three seasons 2016/17, 2017/18 and 2018/19.

Also, on this date, DTS and Mediapro have reached an agreement for the broadcasting of the thematic pay TV channel called “BeIN Sports” containing, among others, matches of the “UEFA Champions League” and “UEFA Europa League” competitions corresponding to the three seasons 2015/16 (from January 12, 2016), 2016/17 and 2017/18.

The total value of the agreements relating to those channels amounts to 2,400 million euros.

Moreover, last December 2, 2015, DTS was awarded the Package number 5 for the pay television broadcast of a live match of First Division and a live match Second Division, exclusively ( first selection), in the tender made by the National Football League and publicly announced on November 13, 2015 for the three seasons 2016/17, 2017/18 and 2018/19.

With this agreement, MOVISTAR+ fulfills its commitment to provide to its entire customer base a comprehensive offer with all the best sports contents.

Madrid, January 12, 2016.

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.