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SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

Report of Foreign Private Issuer

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

of the Securities Exchange Act of 1934

For the month of September, 2015

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 85 48

(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

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Telefónica, S.A.

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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 Stock Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

The Board of Directors has unanimously resolved, preceded by the relevant favourable report from the Nominating, Remuneration and Corporate Governance Committee, the appointment by co-optation of the new Board member Wang Xiaochu, as proprietary Director, to replace Chang Xiaobing, who has voluntarily resigned to his position as Board member of Telefonica, S.A., following his resignation from the positions of Chairman and CEO of China Unicom (Hong Kong) Limited, and the appointment of Wang Xiaochu to such positions.

Madrid, September 30, 2015

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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.