Pearson, 33, began his career at Motherwell before leaving to join Celtic in 2004.
He returned for a second stint at Fir Park in 2015 after spells in England with Derby, Stoke and Bristol City.
"This was something I was really keen to do and I want to thank everyone at Motherwell for the way they've handled this," Pearson said.
"It's with a heavy heart that I go, but at the same time, I am confident the club is in decent shape, with a very good manager and some exciting young talent bubbling under the surface waiting to get their chance, alongside the excellent senior professionals already there.
"I've enjoyed my second spell at Fir Park. I want to thank the fans for all their support and who knows, one day I may be back for another go at it."
Pearson was under contract with Motherwell until October and the Lanarkshire club have received compensation from Atletico de Kolkata.
Motherwell manager Mark McGhee said: "We are desperately disappointed to lose Stephen, but we've known for some time now that this move was on the cards.
"There was absolutely no fall out, it was all extremely amicable, and we understand his personal circumstances. He leaves with the best wishes of everyone at Motherwell FC.
"However, it was then incumbent upon us to try and recoup something to help us find someone else, and that's what we've done. We have been and are engaged in trying to secure a replacement and the midfield area is our priority."
Meanwhile, defender Steven Hammell, Motherwell's post-war record league appearance holder with 530 games, has agreed a new two-year contract.
He said: "I've never made any secret of my feelings for this club, so there is no one happier that my future is sorted out and I can get on with my football."
Motherwell midfielder Stephen Pearson has left the club to join Indian Super League side Atletico de Kolkata.