Algeria striker Slimani joined Leicester from Sporting CP for a reported £28million in 2016 but he has failed to live up to expectations in the Premier League.
The 31-year-old struggled to dislodge Jamie Vardy at King Power Stadium after scoring eight goals in all competitions in his first season in England.
Slimani spent the second half of the following campaign on loan at Newcastle United and was shipped out to Fenerbahce last term.
"I am very happy to be involved with Monaco, a big club that aims to fight for the first places in the championship and to qualify for European competitions," Slimani said.
"I will give everything to help the club achieve its goals."
Slimani won the Africa Cup of Nations in July, appearing as a late substitute as Algeria defeated Senegal in the final.
Reports in England suggest Monaco are closing in on Southampton midfielder Mario Lemina as their next signing.
Leonardo Jardim's men have struggled in the early part of the new season, recording successive 3-0 losses in their opening two fixtures.