Ashwin took 156 wickets at 33.20 apiece in 116 one-day internationals and 72 at an average of 23.22 in 65 T20s.
He was part of the squad that won the 2011 World Cup in India, although he played only two games.
He will be remembered largely for his Test exploits – his tally of 37 five-wicket hauls is second only to Sri Lanka great Muttiah Muralitharan.
Ashwin was the leading wicket-taker in India’s past three series against England, including 24 in the 4-1 home triumph this year.
Captain Rohit Sharma said Ashwin considered retiring before the Australia tour but he convinced him to continue.
Ashwin was left out of the team for the first Test and took one wicket in the second.
“He was very sure about what he wanted to do and the team has complete backing of his thought process,” Rohit said.
“He’s had so many big moments with the Indian team and he’s been a big match-winner for us.
“He’s allowed to make these decisions, and if it is now, so be it.”