EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Tellabs, Inc. (the “Company”) on Form 10-Q for the quarter ended July 3, 2009, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Robert W. Pullen, the Chief Executive Officer of the Company, certify, pursuant to and for purposes of 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Robert W. Pullen

Robert W. Pullen

Chief Executive Officer

Date: August 11, 2009