The 31-year-old reportedly passed a medical on Tuesday.
Slimani joined Leicester, at the time the Premier League champions, for a club record fee in 2016, but struggled, scoring eight goals in the 35 appearances. He went out on loan to Newcastle and last season to Fenerbahce in Istanbul where he scored one league goal.
Slimani was part of the Algeria squad that won the African Cup of Nations in Egypt last month, starting one game and scoring one goal.
The striker will be reunited with former Sporting coach Leonardo Jardim. Slimani broke into the Sporting team in 2013-14, Jardim’s only season at the Lisbon club.
The 31-year-old striker is under contract at Leicester until June 2021. His loan contains a recall clause. He arrives with Monaco last in Ligue 1.
