Mourinho said on the United website that 42-year-old Faria, who he has worked with since 2001, was ideally situated now to become a manager in his own right.
Faria is one of the names who have been linked with filling the large vacuum being left by Arsene Wenger at Arsenal.
"17 years... in Leiria, Porto, London, Milan, Madrid, London again and Manchester," said Mourinho.
"Training, playing, travelling, studying, laughing and also a few tears of happiness.
"17 years and the kid is now a man. The intelligent student is now a football expert, ready for a successful career as a manager."
United -- who round off their Premier League campaign against Watford on Sunday and then face Chelsea in the FA Cup final -- wished him well after his two years at the club.
"#MUFC announces that assistant manager Rui Faria is to leave the club at the end of the season. We wish him all the best for the future," the club tweeted.
Faria, like Mourinho, never played top-level football, but became a significant part of his fellow Portuguese's coaching staff after meeting the future United manager during a seminar day at Barcelona's Camp Nou stadium in 2000.
At the time, Mourinho was assistant to Louis van Gaal at Barcelona but, when he became a manager in his own right at Portuguese club Uniao de Leiria in 2001, he took Faria on as his fitness coach, and the two remained together for spells at Porto, Chelsea, Inter Milan and Real Madrid.
However, Faria's touchline antics have also made him a controversial figure.
In 2014 he was handed a four-game stadium ban for using abusive language towards the officials in a shock 2-1 home defeat for Chelsea at the hands of Sunderland.
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