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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 March, 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 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

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Telefónica, S.A.

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RAMIRO SÁNCHEZ DE LERÍN GARCÍA-OVIES

Secretary General and

of 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 January 23, 2015, in relation to the exclusive negotiations between Telefónica and Hutchison Whampoa Group for the potential acquisition by the latter of Telefónica’s operations in the UK (O2 UK), Telefónica informs that a definitive agreement has been reached after completion of due diligence over O2 UK.

The parties agreed on a purchase price (firm value) of £10,250 million. The equivalent value in euros amounts to approximately €14,000 million at current exchange rate. The price is composed of: i) an initial amount of £9,250 million (approximately € 12,640 million) and ii) an additional deferred payment of £1,000 million (approximately € 1,360 million) to be paid once the cumulative cash flow of the combined company in the UK has reached an agreed threshold. The company intends to allocate a substantial part of the proceeds to achieve a leverage ratio of Net Debt / OIBDA lower than 2.35x.

After the execution of the definitive agreement, O2 UK will be reported as a discontinued operation within Telefónica Group, and its assets and liabilities as “held for sale”, in accordance with IFRS.

Completion of the transaction is subject, among other usual conditions, to the approval of the applicable regulatory authorities and the obtaining of waivers to certain change of control provisions.

The Conditions must be satisfied by no later than June 30, 2016, save that in specified circumstances as set out in the share purchase agreement this date may be extended to 30 September 2016.

Madrid, March 24, 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.