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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 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

Today, TELEFÓNICA, S.A., through its wholly-owned subsidiary TELEFÓNICA EMISIONES, S.A.U., under its Guaranteed Euro Programme for the Issuance of Debt Instruments (EMTN Programme) filed with the Financial Conduct Authority (FCA) in London on June 5, 2015, has launched an issuance of Notes guaranteed by TELEFÓNICA, S.A. in the Euro market amounting to 1,000 million euros.

These Notes, due on September 14, 2021, pay an annual coupon of 1.477% and have a reoffer price of 100%. The settlement and closing date is scheduled for execution on September 14, 2015.

Madrid, September 7, 2015

“This announcement is neither an offer to sell nor a solicitation of an offer to buy any of the securities referred to herein and shall not constitute an offer, solicitation nor sale in any jurisdiction in which such offer, solicitation or sale is unlawful -including but not limited to the United States, Australia, Canada or Japan-.

The securities referred to herein have not been and will not be registered under the United States Securities Act of 1933, as amended, or any state securities laws, and may not be offered or sold in the United States absent registration or pursuant to an exemption from the registration requirements of the Securities Act and in accordance with applicable state securities laws.”

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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.