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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 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

General Secretary and

Secretary to the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA S.A., 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 on 25 March 2015, regarding a share capital increase of Telefónica, S.A., it is informed that on the present day the Spanish National Securities Market Commission (Comisión Nacional del Mercado de Valores) (“CNMV”) has registered in its official records the corresponding securities note, which includes the terms and conditions of the share capital increase and the subscription and disbursement proceeding of the new shares (the “Securities Note”).

The publication of the notice of the share capital increase in the Official Commercial Registry Gazette (BORME) is expected for 27 March 2015. The pre-emptive subscription period for shareholders and acquirers of the pre-emptive subscription rights shall commence on the day following said publication, i.e. 28 March 2015 and shall have a term of 16 calendar days, thus ending on 12 April 2015.

The Spanish prospectus related to the share capital increase composed of the Securities Note and the Registration Document of Telefónica, S.A., registered in the official records of the CNMV on 21 October 2014, is available to the public at the registered office of Telefónica and, in electronic form, both on the CNMV website (www.cnmv.es) and the Telefónica corporate website (www.telefonica.com).

Furthermore, regarding the share capital increase, Telefónica, S.A. informs that a Prospectus Supplement has been filed with the US Securities and Exchange Commission (SEC), which, in addition to the terms of the share capital increase, includes a pro forma financial information section derived from the agreement reached between Telefónica and Hutchinson Whampoa Group for the acquisition by the latter of Telefónica’s operations in the United Kingdom (O2 UK), available to the public on the website of the SEC at the following address:

http://www.sec.gov/Archives/edgar/data/814052/000119312515106994/d894525d424b2.htm

Additionally, Telefónica, S.A. has filed a report on Form 6-K with the SEC that contains the complete wording of the underwriting agreement as an exhibit, also available to the public on the website of the SEC at the following address:

http://www.sec.gov/Archives/edgar/data/814052/000119312515107165/0001193125-15-107165-index.htm

In Madrid, March 26, 2015.

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Disclaimer

This document may not be distributed, directly or indirectly, in any jurisdiction in which said distribution is contrary to the applicable laws.

This document may not be considered as a prospectus and is not an offer or a solicitation to buy, sell, subscribe or exchange the securities issued or to be issued by Telefónica, S.A. No such offer in relation to said securities shall be conducted in any jurisdiction in which said offer is illegal.

Those residents in jurisdictions other than Spain who have access to this document shall seek information regarding the legal restrictions that may be applicable, both relative to the distribution of this document and its content, and shall comply with them accordingly.

This document is not an offer of securities in the United States and the securities referred to herein may not be offered or sold in the United States nor to, on behalf or for the benefit of, any citizen of the United States, as defined in the Regulation S of the US Securities Act of 1933, as amended (“US Securities Act”), unless said offer is registered or falls under an exception of registration pursuant the US Securities Act.

Telefónica, S.A. has filed a registration statement (including a prospectus), with the SEC for the offering to which this communication relates. Before you invest, you should read the prospectus in that registration statement and other documents Telefónica, S.A. has filed with the SEC for more complete information about Telefónica, S.A. and this offering. You may get these documents for free by visiting the SEC web site (www.sec.gov).

This announcement is not a prospectus but an advertisement and investors should not subscribe for any securities referred to in this announcement except on the basis of the information contained in the prospectus.

The authorization to make a public offer of the New Shares in the Republic of Argentina has been requested to the Argentinean National Securities Commission (Comisión Nacional de Valores) (“CNV”) on 11 March 2015, in compliance with the applicable laws and, for the time being, it has not been yet granted. This document is not an offer to sale nor an invitation to conduct an offer to buy, and no purchases or sales of the transferable securities referred to herein may be carried out until the public offer has been authorized by the CNV.

This document is not an offer for sale of securities in the Republic of Peru and the securities referred to herein may not be offered or sold in the Republic of Peru, unless such offer is authorized or falls under an exception of authorization pursuant the applicable law.

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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.