Erik ten Hag's side - who came so close to a place in the Champions League final - needed just a point to win their 34th title.
First-half goals from Lasse Schone and Nicolas Tagliafico ensured that the title was added to their Dutch Cup win.
Dusan Tadic then scored twice - goals in an 11th consecutive league game.
Youssef el Jebli had briefly equalised for the hosts, whose season is not over yet - they go into the relegation play-offs to try and stay in the Eredivisie.
Ajax were again outstanding for long periods in the final appearance for midfielder Frenkie de Jong, who agreed to sign for Barcelona for £65m in January, while captain Matthijs de Ligt is one of several other brilliant young stars who are also expected to leave this summer.
Ajax only missed out on a place in the Champions League final thanks to a stunning last-minute goal from Tottenham's Lucas Moura and Ten Hag may now have a reluctant, if lucrative, rebuilding job on his hands.
Tadic and De Jong both went close early on at the end of typically fluent moves before Schone opened the scoring with a brilliant free-kick from 22 yards.
The hosts responded when El Jebli got the wrong side of De Ligt and fired in at the near post.
But Hakim Ziyech then danced into the area and put a goal on a plate for left-back Tagliafico to regain the lead, and when De Jong won a second-half penalty with a brilliant driving run, former Southampton man Tadic fired in his 37th goal of an unforgettable campaign.
The best was yet to come - Tadic lashing in from a tight angle with a thumping late shot.