The Portuguese coach, who won the Champions League with Porto and Inter Milan, has not worked since his sacking by Italian Serie A side Roma in January.
He was greeted at the airport by a crowd of fans from his new club.
Mourinho was announced the latest move in his career in a post on X on Saturday night from Wembley as he was acting as a television pundit for Real Madrid's 2-0 win over Borussia Dortmund in the Champions League final.
"Good evening Fenerbahce fans, see you tomorrow at Kadikoy (the Istanbul suburb where the club is based) and let's start our journey together," he announced.
Reports suggest Mourinho will sign a two-year contract for Fenerbahce, one of the three big Istanbul sides which has not won the domestic league in 10 years.
Mourinho, who has also managed Chelsea, Manchester United, Tottenham and Real Madrid, 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.
