The 21-year-old, capped by France at every level from Under-16 to Under-21, had joined City's academy from Le Havre in 2012.
The midfielder has spent the last two seasons on loan at Genoa, scoring three goals in 37 Serie A appearances.
Ntcham did not manage a senior appearance for City and will now seek to help Celtic retain the Scottish Premiership title.
"It's a nice feeling to be here at Celtic and I want to win everything at Celtic as I have never won a trophy before," he said in a statement.
"I'm most looking forward to the derby and playing in the Champions League. I remember them beating Barcelona five years ago in the group stages. Not every club gets to play in this competition so I'm happy to have the chance to play there with Celtic.
"Celtic is a fresh challenge for me. While Genoa are a good team, I knew they wouldn't win Serie A as they were not a top team like Juventus, but I know Celtic are a big team in Scotland."