The centre half, who can also play at full back, is set to play with the Championship club permanently.
Tanganga was on loan with the Lions in the second half of the season, helping them to stay in the Championship.
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Per The Mirror, Spurs are happy to let the homegrown defender leave to get regular football.
Tanganga played 18 games for Millwall during the latter part of this term, having struggled at Augsburg on loan for the first half of the campaign.
Millwall head coach Neil Harris was eager to hold onto the defender and appears to have gotten his wish.