The 18-year-old Cameroon youth international has agreed terms on a three-year deal and will arrive at Ajax on a free transfer when his Barcelona contract expires in June.
Onana has been in Barcelona's youth system since 2010 and this season was promoted to their Under-19 team, but he has not played a senior game.
He caught the eyes of the Dutch side when he played for Barcelona against Ajax in November in the Uefa Youth League, the continental youth competition for clubs competing in the Champions League, and the four-time European champions have swooped in ahead of other interested teams.
The Cameroon-born Onana joined the famous Barcelona La Masia academy through a link with the Samuel Eto'o football foundation in Cameroon.
Compatriot Fabrice Ondoa, 19, is expected to be first choice for Cameroon at this month's Africa Cup of Nations in Equatorial Guinea even though he has yet to make a first-team appearance for Barcelona.
Barcelona youth goalkeeper Andre Onana has signed a pre-contract agreement to join Ajax in July, the Dutch champions announced on Saturday.