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."

The review "paves the way for changes" to the current system, which has been in place since 1988, the Treasury said.
However, the outcome is expected to be fiscally neutral, meaning that the total sum collected from businesses will not change.
The review was first announced in December's Autumn Statement.
"The time has come for a radical review of this important tax. We want to ensure the business rates system is fair, efficient and effective," said Danny Alexander, chief secretary to the Treasury.
The Treasury said the review will look at how firms use property, what the UK could learn from other countries and how the system could be modernised to better reflect changes in property values.
"Lots and lots of people have views about how the business rates system doesn't work, but as soon as you get into what an alternative system might look like there's much less consensus," Mr Alexander added, speaking to the BBC's Wake up to Money programme.
Labour's shadow exchequer secretary to the Treasury Shabana Mahmood said: "Britain's businesses need more than just a re-announced review. Labour will take immediate action by cutting and then freezing business rates for 1.5 million small business properties."
The announcement follows widespread criticism of the current system, where rates are charged to retailers based on the value of their shop or other commercial property.
The arrangement means that companies with similar turnovers can pay dramatically different sums for business rates because their properties have varying "rateable values" depending on the size and location of their premises.
John Cridland, director-general of the CBI, said the current system of business rates was "outmoded, clunky and regressive" and "holding back the high street".
"We'll be making the case for removing the smallest firms from paying business rates completely... and introducing more frequent valuations," he said.
John Longworth, director general of the British Chambers of Commerce, welcomed the review, but said "actions speak louder than words".
"Unless a root and branch reform of business rates is delivered at Budget 2016, firms will regard this as a missed opportunity to tackle a huge brake on investment and growth," he added.
The rates paid by English businesses are the highest of any European Union country and can be a company's biggest expense after wages and rent.
Rates have been blamed for the decline of many High Streets and the rising number of vacant shops.
Business rates are calculated according to the rental value of the property a company uses. They date back to the Poor Law established in 1601.
Current valuations are still based on property prices in 2008, before the economic downturn hit the value of commercial real estate, as the government postponed a revaluation scheduled for last year.
Motherwell midfielder Stephen Pearson has left the club to join Indian Super League side Atletico de Kolkata.
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A "radical" review of the business rates system in England has been launched, with its findings due in time for the Budget in 2016.