The 38-year-old took 537 wickets in his 106 Tests at an average of 24.00, leaving him seventh on the all-time list and second only to Anil Kumble (619) for his country.
He also played 116 one-day and 65 Twenty20 internationals.
"This will be my last day as an Indian cricketer in all formats at an international level," Ashwin said at the post match press conference alongside skipper Rohit Sharma after the match was drawn.
"I feel there's a little bit of punch left in me as a cricketer, but I'd like to express that, showcase that, in club-level cricket."
He was not selected for Brisbane with his final Test coming in Adelaide last week where he took 1-53.
"I've had a lot of fun. I have made a lot of memories alongside Rohit and several of my team-mates," he added.
"Obviously there are a lot of people to thank, but I will be failing in my duties if I didn't thank the BCCI and fellow team-mates."
Rohit said Ashwin had decided to call it a day during the Perth Test but he had persuaded him to stay on for Adelaide.
However, he decided during this Test that his time as an international cricketer was over.
"As a team we have to respect that decision," Rohit said.
"He was very sure about what he wanted to do and the team has complete backing of his thought process.
"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."
Australian captain Pat Cummins said Ashwin had been a fierce competitor.
"He's obviously been a fantastic player all around the world -- there aren't that many finger spinners that have that kind of longevity," Cummins said.
"He'll go down as one of the all-time greats.
"There's a massive respect from our change room for the career that he's had."
Ashwin made his Test debut in 2011 against the West Indies and was also handy with the bat, scoring 3,503 runs with six centuries and 14 fifties.
