After the first leg finished 1-1, the Dutch Eredivisie outfit progressed to the semi-final after goals from Donny van de Beek and Matthijs de Ligt gave them a 3-2 aggregate win at Allianz Stadium.
While celebrating the triumph, the 23-year-old warned their next opponent - winner of the tie between Manchester City and Tottenham Hotspur - that their 'journey' for their first European title since 1995 hasn't come to an end.
"This amazing journey isn’t ending just yet! Very proud of this team & all your support. One last thing, Ajax are in the semi-finals," Onana tweeted.
The Indomitable Lions will begin the campaign for their fifth continental title with their opening fixture against Guinea-Bissau on June 25 before taking on Ghana and Benin on June 29 and July 2 respectively.