The left-handed Wadekar captained India's Test and one-day international sides, leading his country to wins over England and the West Indies in 1971.
After finishing his playing career, he later became coach, manager and selector of the national side.
Indian prime minister Narendra Modi praised Wadekar's contribution to cricket on Twitter, calling him a "great batsman and wonderful captain".
Modi also stated that Wadekar "led our team to some of the most memorable victories in our cricketing history", saying he was "pained by his demise".
Former player and current Indian head coach Ravi Shastri also tweeted his condolences about Wadekar's death.
Wadekar scored 2,113 runs in 37 Test matches, spanning between 1966 and 1974.