The Portuguese coach, who won the Champions League with Porto and Inter Milan, has not worked since he was sacked by Italian Serie A side Roma in January.
He has also managed Chelsea, Manchester United, Tottenham and Real Madrid.
"Good evening Fenerbahce fans, see you tomorrow at Kadikoy (the Istanbul suburb where the club is based) and let's start our journey together," Mourinho posted on his new club's X account.
The Portuguese confirmed the move as he was acting as a pundit for TNT Sports television at the Champions League final at Wembley.
According to Turkey's NTV television station, Mourinho's appointment is due to be made official on Sunday.
Reports suggest Mourinho will sign a two-year contract for Fenerbahce, one of the three big Istanbul sides which have not won their domestic league in 10 years.
Mourinho was dismissed by Roma after two-and-a-half years in January with the club struggling in ninth at the time.
He guided Roma to the inaugural Europa Conference League trophy in 2022 and the final of last season's Europa League.