The 21-year-old winger has signed a five-year contract, until 2021, Spurs announced.
"We are delighted to announce the signing of Georges-Kevin Nkoudou from Marseille," Tottenham said.
Spurs' Clinton Njie has moved in the opposite direction on loan, Marseille announced.
Nkoudou made 40 appearances in two seasons with Nantes before joining Marseille in June 2015.
The France under-21 international impressed with OM, scoring 10 times in 41 appearances and struck four goals in the Europea League.
Nkoudou agreed personal terms with Spurs last month and has been training at Hotspur Way as the two clubs finalised the transfer
The £11million deal was delayed by a change of presidency at Marseille.
Nkoudou may not be Tottenham's final summer acquisition, with boss Mauricio Pochettino keen on another addition after the recent sales of Nacer Chadli, Nabil Bentaleb and Ryan Mason.
Spurs on Tuesday ended their interest in signing Crystal Palace winger Wilfried Zaha after an initial £12m offer was rejected last week.
Newcastle's Moussa Sissoko was one option being considered but Spurs want Newcastle to lower their £35million asking price and it appeared the France midfielder was more likely to leave for Everton on Wednesday evening.
Source : PA
Source: PA