The buyback programme, which was passed through a special resolution, saw 99.81 per cent of the total number of valid votes being cast in favour of the proposal, the company said in a regulatory filing.
The nod comes ahead of TCS' fourth quarter and full fiscal (2016-17) results, scheduled to be announced tomorrow.
The share buyback, if successful, will be India's biggest, surpassing Reliance Industries' 2012 share repurchase of Rs 10,400 crore.
The Indian IT companies have been under pressure to return excess cash on their books to shareholders through generous dividends and buybacks.
TCS had earlier said that it received suggestions from investors over the need for certainty on dividend policy along with share buyback to distribute the cash.
The Mumbai-based company has a cash pile of Rs 43,169 crore, which is nearly 10 per cent of the company's market capitalisation.
Last week, Infosys announced its capital allocation policy to return up to Rs 13,000 crore this financial year through dividend and/or buyback.
Smaller peer HCL Technologies has also approved a buyback of up to 3.50 crore shares worth Rs 3,500 crore.
In the filing today, TCS said, there was 100 per cent voting in favour of the resolution by the promoter and promoter group, while 99.03 per cent votes of the institutional holders were cast in favour of the buyback. Amongst public shareholders, there was 97.51 per cent votes in agreement.
The proposed shares under the buyback represent 2.85 per cent of the total paid-up capital at Rs 2,850 per equity share.
The buyback is proposed to be made from the shareholders of the company on a proportionate basis under the tender offer route using the stock exchange mechanism, TCS had said earlier.
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