The Bengaluru-based company has fixed September 15 as the the record date for the buyback offer.
It had said last month that it will purchase up to 343.75 million shares at Rs 320 (USD 4.95) per scrip. The total size of the offer will be up to Rs 11,000 crore (USD 1.7 billion).
"The aforesaid special resolution has been passed through postal ballot and e-voting by members by requisite majority," Wipro said in a filing to the BSE.
The voting, which ended on August 28, saw 99.68 per cent of the votes being cast in favour of the buyback offer.
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Wipro shares closed marginally higher at Rs 291.65 on the BSE.
Share buybacks improve earnings per share and return surplus cash to shareholders while also supporting share price during periods of sluggish market conditions.
As on June 30, 2017, Wipro had 'cash and cash equivalents' of Rs 5,432 crore on its books and 'investments' of Rs 31,772 crore, totalling Rs 37,204 crore.
Among Indian IT companies, TCS, which had a cash kitty of over Rs 43,000 crore, has already completed a Rs 16,000 crore buyback programme earlier this year.