The Turkish club revealed the arrival of the Algeria international on their official website, though Leicester, who opened their Premier League season with a 2-1 loss to Manchester United, are yet to confirm the deal.
According to Fenerbahce, Slimani will join them on loan for the 2018-19 season after completing a medical and signing a contract.
The forward scored 39 goals in his final two full seasons with Sporting, including 27 in his final campaign, but never found the same level in the Premier League.
Slimani did manage seven goals in 23 games, 13 of those starts, in his first year in the Premier League with the Foxes.
But his second season was a struggle, as he managed just one goal for Leicester in 12 games and only two starts.
A January loan to Newcastle offered a new chance on paper, but in practice Slimani found life just as difficult, as he did not score in four appearances for the club, making just one start.
Reports swirled this summer of Slimani's exit from the King Power stadium, with a return to Sporting among the rumoured destinations along with options in the Turkey.
And Fenerbache has apparently landed won that race, and will hope Slimani rediscovers the form that made him a star in Portugal.