Club Brugge and Slavia Prague also advanced to the Champions League draw with home wins on Wednesday.
Amsterdam: Edson Álvarez, the defender Ajax bought to replace departed captain Matthijs de Ligt, scored the decisive goal Wednesday to give the Dutch team a place in the Champions League group stage.
Alvarez, a 21-year-old Mexico international, guided the 43rd-minute header into APOEL's net to open the scoring in a 2-0 win in the second leg of their playoff.
Ajax's new captain, playmaker Dusan Tadic, struck with a powerful shot in the 80th to complete the 2-0 aggregate victory for last season's semifinalist.
Alvarez cost Ajax a reported USD 17 million from Mexican club America last month, helping replace 20-year-old De Ligt who joined Juventus in a 75-million euro ($85-million) off-season deal.
Club Brugge and Slavia Prague also advanced to the Champions League draw with home wins on Wednesday. Brugge beat LASK Linz 2-1 for a 3-1 aggregate win, and Slavia's second 1-0 win over CFR Club made it 2-0 on aggregate. The losing play-off teams will enter the 48-team Europa League group stage, which is drawn Friday.