Barcelona and the Amsterdam club have reached an initial agreement to complete the move, with a deal expected to be finalised soon.
The main sticking point has been how to split the goalkeeper's high wages. That issue is now largely resolved, though some details remain to be settled elsewhere. Ter Stegen must still pass a medical in Amsterdam to confirm he has fully recovered from injury.
Ajax could not take on the roughly €20 million Ter Stegen earns at Barcelona, so the Spanish club will continue covering the bulk of his salary. Ajax will pay just over 10% of the goalkeeper's wages under the proposed arrangement.
A similar structure was used last season when Ter Stegen joined Girona on loan, with Barcelona covering a comparable share of his pay. Ajax head coach Míchel worked with Ter Stegen at Girona and pushed for the move at both clubs.
Míchel had already signed Ter Stegen for Girona last season and has now succeeded in bringing him to Amsterdam. Ter Stegen has fallen behind Joan García in Barcelona's pecking order.
García has become first-choice goalkeeper under head coach Hansi Flick after a strong season.
Míchel is prepared to guarantee Ter Stegen the number one jersey at Ajax, just as he did at Girona. Ter Stegen still has two years remaining on his Barcelona contract.
The Germany international travelled to Barcelona on Thursday aware the agreement was close.
He is expected to fly to Amsterdam to join Ajax training once the move is finalised.