Haller was picked up by Dortmund officials after landing at the city’s airport and taken for his medical.
The 28-year-old Ivory Coast international is reportedly set to sign a four-year deal with Dortmund to replace Haaland, who has joined Premier League champions Manchester City.
German daily Bild say Haller’s transfer from Ajax is set to cost Bundesliga runners-up Dortmund around 31 million euros ($32.5 million) including bonuses.
According to magazine Kicker, the transfer will be finalised in July so Ajax can add the income earned to their books in the new financial year.
Haller was in superb form in the Champions League last season, scoring 11 goals in eight games including four in a 5-1 win over Sporting Lisbon in Ajax’s opening group match.
He scored in both games against Dortmund as Ajax beat the German club home and away in the group stage.
The Dutch champions bowed out in the last 16, but Haller went on to score 21 goals in 31 games in the Eredivisie.
Haller is set to follow on from strikers Robert Lewandowski, Pierre-Emerick Aubameyang and Haaland, who all matured into top stars during stints playing for Dortmund.