The 38-year-old slow-bowler ends a 16-year association with the franchise tournament in his home country, where he is currently the fifth-highest wicket-taker with 187 scalps.
Ashwin played most of his IPL career for his home side Chennai Super Kings - with who he won the trophy in 2010 and 2011 - but he also represented Rising Pune Supergiant, Delhi Capitals and Rajasthan Royals and captained Kings XI Punjab (now Punjab Kings).
He retired from all international cricket in December last year as India second-highest leading wicket-taker in Test matches.
The BCCI doesn't allow any current player in Indian international or domestic cricket to feature in overseas T20 leagues.
Ashwin wrote on social media: "They say every ending will have a new start, my time as an IPL cricketer comes to a close today, but my time as an explorer of the game around various leagues begins today.
"Would like to thank all the franchisees for all the wonderful memories and relationships over the years and most importantly the @IPL and the @BCCI for what they have given me until now.
"Look forward to enjoying and making the most of what's ahead of me."
He will now have the option to sign up for leagues such as the BBL in Australia, the SA20 in South Africa, The ILT20 in the UAE, the Hundred in England and the CPL in the West Indies.