The 23-year-old wasted no time to make an impact and scored the decisive goal at his first start for Milan in a 1-0 win over Verona.
Gimenez joined the Serie A Giants for £ 25 million after Feyenoord agreed to a sale in the middle season, after the strong desire of the player to move.
According to Calciomercato, Spurs made a late attempt to hijack the transfer as they are scrambling for attacking reinforcements.
Ange Postecoglou ultimately protected Mathys Tel on loan with an option to buy for £ 45 million, although the negotiations were tense in the last days.
Despite their efforts, Tottenham Gimenez, who now stands his former club in the play-off second stage of the Champions League.