The French Ligue 1 side did not disclose the duration of the contract or the financial details of the transfer.
Reports in British media said Schmeichel has signed a three-year deal with Nice, who had reportedly agreed to pay Leicester £1million ($1.21 million) for the player.
"OGC Nice is delighted with the arrival of the UEFA Euro 2020 semi-finalist," Nice said in a statement.
Schmeichel, who joined Leicester in 2011 from Leeds United, helped them to the 2015-16 Premier League title, as well as their maiden FA Cup win in 2021.
Following 479 games played for the Foxes during 11 seasons, he sits third in Leicester's all-time appearance list.
He made his international debut in a 3-0 friendly win over Macedonia in 2013 and has been capped by 2020 Euro semi-finalists Denmark more than 80 times.
The Denmark international has become Nice's third arrival this week after they announced Welsh midfielder Aaron Ramsey on a free transfer on Monday, and defender Mattia Viti from Serie A side Empoli earlier on Wednesday.
