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, 2017

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  ☒            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  ☒

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  ☒

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  ☒

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): N/A

Telefónica, S.A.

TABLE OF CONTENTS

RAMIRO SÁNCHEZ DE LERÍN GARCÍA-OVIES

General Secretary and

Secretary to the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA, S.A. (“Telefónica”) as provided in article 228 of the Spanish Stock Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

In relation to the bonds mandatorily convertible into shares of Telefónica, S.A. that were issued by its wholly-owned subsidiary Telefónica Participaciones, S.A.U. on September 24, 2014, guaranteed by Telefónica (the “Bonds”), and which were referred to in the Significant Events of September 10, 2014 and of September 11, 2014, Telefónica announces that, in order to attend the mandatory conversion of the totality of the Bonds on their maturity date on September 25, 2017, and given the resulting conversion price of EUR 9.7174 per share:

As a result of the conversion and the aforementioned capital increase, Telefónica’s share capital is set at 5,192,131,686 euros, divided into 5,192,131,686 ordinary shares of the same class and series, with a nominal value of 1 euro, and the Bonds will be fully amortized.

The public deed of conversion of obligations, capital increase and amortization of obligations has been registered with the Mercantile Registry of Madrid today.

It is expected that the New Shares will be admitted to trading on the four Spanish Stock Exchanges and will be tradable through the Spanish Automated Quotation System (Sistema de Interconexión Bursátil Español) on September 25, 2017. The admission to trading of the New Shares in the remaining foreign Stock Exchanges where Telefónica is listed will also be requested.

Madrid, September 20, 2017

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.