The Turkish club revealed the arrival of the Algeria international on its official website, although Leicester is yet to confirm the deal.
But the forward was in attendance as the Istanbul club began its new Super Lig campaign with a come-from-behind win over Bursaspor on Sunday (AEST), suggesting Leicester's confirmation is just a matter of time.
According to Fenerbahce, Slimani will join the club on loan for the 2018/2019 season after completing a medical and signing a contract.
The 30-year-old scored regularly during his time with Sporting in Portugal but struggled for goals in England, managing just eight for Leicester in the Premier League.
He spent the second half of the 2017/2018 campaign on loan to Newcastle United, failing to find the net in four appearances.