The Serie A club made the shock announcement of Mourinho’s appointment just over two weeks after he was sacked by English Premier League side Tottenham Hotspur, and a few hours after confirming Fonseca's exit.
"For me, professionalism is a sacred value. I am as motivated here today as I was on my first day. I want to do my best for Roma until the final day," Fonseca told a news conference.
"Mourinho is a great coach, we all know that. I think he will do a great job.
How London 2012 inspired Team GB's Leah Williamson to become an Olympian
"Speaking honestly, I thought it was time to follow a different path away from Roma."
Fonseca's side face Manchester United in the second leg of their Europa League semi-final in Rome on Thursday, but have a mountain to climb to reach the final after losing 6-2 at Old Trafford last week.
"It's not easy to beat Manchester United 4-0, but I've seen many things happen in football. I believe in everything," Fonseca said.
Van Dijk set for Liverpool return in friendly with Hertha
Tottenham confirm Gil deal, with Lamela heading to Sevilla