De Telegraaf reports that the two clubs reached an agreement on Sunday for the 27-year-old to return to Amsterdam.
Werder will receive an initial fee of €11m with €3m to potentially follow in bonuses.
The Bundesliga side were reluctant to sell Klaassen, but he pushed for a move back to Amsterdam.
It took three bids from Ajax to convince Werder to sell the Dutch international, who arrived from Everton in 2018.
Klaassen has agreed a four-year contract with Ajax and will accept a lower salary than he has been earning.
He was given permission to skip training this morning and is heading to Amsterdam to finalise his move.
A product of the club’s famous academy, Klaassen was transferred to Everton in 2017 but after a year joined Werder.