Ajax were eight points behind joint leaders PSV Eindhoven and AZ Alkmaar in mid-February before their unstoppable run.
He has goals for AZ Alkmaar in the Netherlands, a record for an American in a European season.
Arsenal were drawn in Group H alongside Dutch side AZ Alkmaar, Greek side Olympiakos and Belgium's Standard Liege.
Arsenal have been drawn against AZ Alkmaar, Olympiakos and Standard Liege, while Rangers will play Sevilla, Stuttgart and Unirea Urziceni.
Dutch club AZ Alkmaar claimed they have a pre-contract agreement with Alves.
In the other group match, Vassilis Torosidis scored a late header to give Greek champions Olympiakos a 1-0 win over AZ Alkmaar.
But Celtic cancelled their planned friendly against AZ Alkmaar on Wednesday night.
Despite the defeat, Standard Liege can still reach the knockout stages after AZ Alkmaar and Olympiakos drew 0-0 in the other group match.
On Saturday, Twente won 1-0 at Den Haag while defending champions AZ Alkmaar joined Ajax on six points with a 6-0 trouncing of pointless Waalwijk.
The Romanian side, along with Wolfsburg, Rubin Kazan, AZ Alkmaar, Standard Liege, Debrecen, APOEL Nicosia and FC Zurich, make their Champions League debut in this year's tournament.
However, if Arsenal win at Olympiakos in the final group match -- and Liege defeat AZ Alkmaar at home, the Belgian side will snatch second place on head-to-head records.
The other group match ended in a draw, as Standard Liege substitute Moussa Traore scored a last-gasp equalizer to earn the Belgian side a 1-1 draw with Dutch champions AZ Alkmaar.
Several players have been targets of abuse from supporters in recent weeks, including American forward Jozy Altidore of the Dutch club AZ Alkmaar, Barcelona defender Daniel Alves and AC Milan midfielder Kevin-Prince Boateng, who led his teammates off the field during an exhibition game in protest.
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