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It marks a swift return to management for the Portuguese, who was sacked by Tottenham on April 19 after a disappointing 17 months in charge. He left Spurs with a 51 per cent win ratio in all competitions - only with Leiria (45 per cent) at the start of his managerial career had he posted a worse return.
However, Mourinho won two league titles, the Coppa Italia twice and a Champions League during his only previous spell in Italian football, which was with Inter between 2008 and 2010.
Fonseca expects his successor to do well during his time in the Italian capital.
"He is a great coach, we all know that. I think he will do a great job," Fonseca said at a news conference on Wednesday previewing his side's Europa League clash with Manchester United.
Asked if the decision to step down at the end of the season was mutual, Fonseca replied: "Speaking honestly, I thought it was time to follow different paths with Roma.
"It is not one of the most difficult tests of my career, I live this moment with normality, as a professional focused on my work until the last day.
"For me, professionalism is a sacred value. I am here today as on the first day: motivated. I want to make the best of Rome until the last day."
Fonseca guided Roma to a fifth-placed finish in the 2019-2020 season but it sits seventh this campaign, 14 points adrift of the Champions League qualification places.
An impressive run to the Europa League semi-finals appears likely to come to an end on Thursday, however, as United lead 6-2 heading into the second leg in Rome.
Yet Roma famously overturned a 4-1 first-leg deficit to knock Barcelona out of the Champions League quarter-finals in 2018 and Fonseca is not ruling out another miracle result.
"It's not easy to beat Manchester 4-0, but I've seen a lot of things in football. I believe in everything," he said.
Roma has not lost both legs of a two-legged knockout tie in major European competition (excluding qualifiers) since the 2015-16 Champions League last-16 meeting with Real Madrid.