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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 July, 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., (hereinafter “Telefónica”) pursuant to article 82 of the Spanish Securities Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

In relation to the Significant Event filed yesterday, for the purposes of Article 531 of the Spanish Corporation Act (Ley de Sociedades de Capital), it is attached as an appendix to this Significant Event, the literal transcription of the clause 2.5 of the agreement signed between Telefónica and Vivendi, S.A.

Madrid, July 30, 2015.

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TRANSCRIPCIÓN LITERAL DE LA CLAUSULA 2.5 DEL ACUERDO SUSCRITO ENTRE TELEFONICA, S.A Y VIVENDI, S.A. CON FECHA 29 DE JULIO DE 2015

2.5 Vivendi Parties’ Commitment.

2.5.1 The Vivendi Parties commit:

2.5.1.1 until August 30^th (the “First Lock up Period”) with respect to 100% of the Telefónica Swap Shares;

2.5.1.2 until the later of (a) September 30^th, 2015 or (b) thirty (30) days after Closing; (the period between the Closing Date and the later of (a) and (b) hereinafter referred to as the “Second Lock up Period”), with respect to 100% of the Telefónica Swap Shares;

2.5.1.3 until the later of (a) November 30^th, 2015 or (b) ninety (90) days after Closing; (the period between the Closing Date and the later of (a) and (b) hereinafter referred to as the “Third Lock up Period”), with respect to 50% of the Telefónica Swap Shares; and

2.5.1.4 during the fifteen (15) calendar day period prior to (and including) any Quarterly Results Announcement Date (the “Results Black Out Period”), with respect to any Telefónica Swap Shares;

not to, directly or indirectly, offer, pledge, sell (including, but not limited to, through any type of transactions regarding derivatives, options, swaps, futures, collaterals, securities lending or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of shares in Telefónica), contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend or otherwise transfer or dispose of, directly or indirectly (including through participation certificates, depositary or other receipt instrument, right or entitlement representing shares in Telefónica), any of such Telefónica Swap Shares, whether any of those transactions is to be settled by delivery of shares in Telefónica or such other securities, in cash or otherwise.

2.5.2 After the expiry of the First Lock-up Period or Second Lock-up Period or Third Lock-up Period, the Vivendi Parties are authorized to sell and transfer the Telefónica Swap Shares, subject to the provisions of Articles 2.5.1.2, 2.5.1.3 and 2.5.1.4, in an orderly market manner, except that the Vivendi Parties shall not sell the Telefónica Swap Shares in any private transaction to a telecommunication service provider or any affiliate thereof. The Vivendi Parties commit not to sell (including, but not limited to, with respect to any type of transactions regarding derivatives, options, swaps, futures collaterals or securities lending) in any day, directly or indirectly, on any market where the Telefónica shares are traded, any Telefónica Swap Shares in an aggregate amount in excess of 15% of the total amount of the Telefónica shares sold in the Madrid Stock Exchange on such day (excluding block trades and cross trades).

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2.5.3 The Vivendi Parties assume the commitments in Article 2.5.1.1 for the benefit of Telefónica and of the entities that acted as Joint Global Coordinators, on behalf of the entities acting as Underwriters, in the offering of shares of Telefónica, S.A. approved by the board of directors of Telefónica, S.A. on March 25, 2015.

2.5.4 The Parties hereby acknowledge and agree that the commitments assumed by the Vivendi Parties in Article 2.5.1 shall not apply to (a) any transfer or sale (including, but not limited to, through any type of transactions regarding derivatives, options, swaps, futures, collaterals, securities lending or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of shares in the Telefónica Swap Shares) of Telefónica Swap Shares by the Vivendi Parties to any Affiliate of the Vivendi Parties provided that (i) the transferee (“Vivendi Affiliate Transferee”) shall agree to become bound by all the obligations of the Vivendi Parties under this Article 2.5, and (ii) the Vivendi Parties remain jointly and severally liable for any action, omission, obligation or breach by the Vivendi Affiliate Transferee; and/or (b) the tendering of the Telefónica Swap Shares to a public tender offer relating to Telefónica launched by a third party that is not an Affiliate of the Vivendi Parties.

2.5.5 The Vivendi Parties shall notify Telefonica in writing as soon as possible once they have transferred, sold or otherwise disposed of 100% of the Telefonica Swap Shares.

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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.