Ajax will pay Bremen 11 million euros ($13 million), which could rise to 14 million euros with bonuses, for Klaassen who came through the Dutch giants’ academy.
“It was clear to us that we would not let Davy go at any price, but only if our expectations were met, especially since he was one of our top performers,” said Bremen director Frank Baumann.
“That has happened and we were able to fulfil Davy’s wish to switch to Ajax, because he sees his sporting home as being there.”
The 27-year-old joined Bremen from Everton in 2018 as the German club’s record transfer at a cost of around 13.5 million euros.
He has scored 16 goals, created 13 more in 81 appearances for the north German side and captained the team to Saturday’s 1-0 win over Arminia Bielefeld.
He made his professional debut for Ajax in 2011, winning three Dutch league titles and making 180 appearances and scoring 55 goals before joining Everton in 2017.
He has played 16 times for his national team, although his last appearance for the ‘Oranje’ was back in 2017.