Waiver of Certain Rights in Connection with the Share Purchase

Exhibit 10.6

August 2, 2012

N.V. Tyagarajan

c/o Genpact International, Inc.

105 Madison Avenue

New York, NY 10016

Waiver of Certain Rights in Connection with the Share Purchase

Dear Tiger:

As you are aware, South Asia Private Investments (“Investor”), a Mauritius private company limited by shares and an affiliate of Bain Capital LLC, has entered into a Share Purchase Agreement, dated as of August 1, 2012, (“Share Purchase Agreement”) with certain affiliates of General Atlantic LLC (collectively, “General Atlantic”) and certain affiliates of Oak Hill Capital Management, LLC (collectively, “Oak Hill”) pursuant to which Investor will purchase a substantial portion of the common shares (the “Common Shares”) of Genpact Limited (the “Company” and such purchase, the “Share Purchase”) owned by General Atlantic and Oak Hill and thereby make a significant investment in the Company. As a result of the Share Purchase, Investor could acquire beneficial ownership of 25% or more of the voting securities of the Company.

You currently hold (i) restricted share units in respect of 200,000 Common Shares granted to you under the Restricted Share Unit Issuance Agreement, dated as of June 15, 2011 (the “RSU Agreement”), of which 50,000 became vested on June 17, 2012 (the unvested restricted share units, the “RSUs”), (ii) a performance share award in respect of a maximum of 150,000 Common Shares and with respect to which the target payment is 100,000 Common Shares (the “2011 PSUs”) granted to you under the Performance Share Award Agreement, dated as of June 15, 2011 (the “2011 PSU Agreement”), none of which have vested, (iii) a performance share award in respect of a maximum of 150,000 Common Shares and with respect to which the target payment is 100,000 Common Shares (the “2012 PSUs,” together with the 2011 PSUs, the “PSUs”) granted to you under the Performance Share Award Agreement, dated as of March 6, 2012 (the “2012 PSU Agreement,” together with the 2011 PSU Agreement, the “PSU Agreements”), none of which have vested and (iv) share options to purchase 250,000 Common Shares (“Options” and together with the RSUs and PSUs, the “Equity Awards”) granted to you under the Share Option Agreement, dated as of June 15, 2011, of which 62,500 have vested (the “Option Agreement”, together with the RSU Agreement and the PSU Agreements, the “Equity Award Agreements”), in each case, subject to the terms and conditions of the applicable Equity Award Agreement and the Genpact Limited 2007 Omnibus Incentive Compensation Plan (the “Plan”) and pursuant to the employment agreement, dated as of June 15, 2011, by and between you and the Company (the “Employment Agreement”).

The Share Purchase would constitute a “Change of Control” under the terms of the Plan, the Employment Agreement and the Equity Award Agreements. However, the Company’s Board of Directors has determined that the Share Purchase is not the type of transaction that should constitute a Change of Control for purposes of the Plan. For this and other reasons, the Company requests, in connection with the Share Purchase, that you consent to the treatment of the Equity Awards, in each case, as outlined in this letter agreement.

For good and valuable consideration, the receipt and sufficiency of which you hereby acknowledge, in accordance with Sections 7(a) and 7(b) of the Plan, and notwithstanding Section 8 of the Plan, Section 5 of the Employment Agreement, Section 4 of the RSU Agreement, Section 3(e) of the 2011 PSU Agreement, Section 4 of the 2012 PSU Agreement and Section 3(c)(ii) of the Option Agreement, you hereby agree to and acknowledge the following modifications of the Plan and the Equity Award Agreements.

(1) You agree that, (A) the consummation of the Share Purchase (the “Closing”) shall not constitute a Change of Control for purposes of the RSUs, (B) the RSUs shall remain outstanding and shall continue to vest after the Closing in accordance with the RSU Agreement and (C) the RSUs shall remain subject to the terms and conditions of the RSU Agreement, except as specifically provided in this letter agreement; provided, however, that in connection with and in consideration for your waiver of the accelerated vesting of the RSUs in connection with the Share Purchase pursuant to Section 4 of the RSU Agreement, you shall be granted an additional 30,000 RSUs (the “Additional RSUs”) as soon as practicable after the Closing and such Additional RSUs shall be subject to the same terms and conditions as the RSUs, except that the Additional RSUs shall vest on December 31, 2016 provided that you remain in employment or service with the Company on such vesting date. The number of Additional RSUs shall be adjusted to reflect the Company’s special dividend of $2.24 per share in the same manner as other outstanding equity awards under the Plan.

(2) You agree that, (A) the Closing shall not constitute a Change of Control for purposes of the PSUs, (B) the PSUs shall remain outstanding and shall continue to vest after the Closing in accordance with the applicable PSU Agreement and (C) the PSUs shall remain subject to the terms and conditions of the applicable PSU Agreement, except as specifically provided in this letter agreement. In connection with and in consideration for your waiver of the accelerated vesting of the PSUs in connection with the Share Purchase pursuant to Section 3(e) of the 2011 PSU Agreement and Section 4 of the 2012 PSU Agreement, as applicable, you shall have, consistent with the current terms of the applicable PSU Agreement, the opportunity to earn up to the maximum number of Common Shares payable in respect of each of the PSUs (i.e., up to 150% of the target payment under the applicable PSU Agreement) on the applicable vesting date set forth in the applicable PSU Agreement.

(3) You agree that, (A) the Closing shall not constitute a Change of Control for purposes of the Options, (B) the Options shall remain outstanding after the Closing and shall continue to vest after the Closing in accordance with the Option Agreement and (C) the Options shall remain subject to the terms and conditions of the Option Agreement, except as specifically provided in this letter agreement.

(4) You agree that, for the purposes of the Plan and the Equity Award Agreements, (a) the Share Purchase shall not constitute a Change of Control and (b) solely with respect to Investor (or any of its affiliates or successors), the 25% thresholds in the definition of Change of Control under the Plan (and any award agreement to which you may be, or become, a party) shall instead be 50% thresholds.

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(5) You agree that, in the event the Share Purchase Agreement terminates and the Share Purchase is not consummated, (A) this letter agreement shall, upon the termination of the Share Purchase Agreement, immediately become void ab initio and shall have no further force or effect and (B) all obligations of the Company and its affiliates and any rights that you may have pursuant to this letter agreement shall terminate.

To indicate your agreement with the foregoing, please sign and date the attached copy of this letter agreement.

Agreed and Acknowledged as of

this 2nd day of August, 2012

/s/ N.V. Tyagarajan

N.V. Tyagarajan

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