"After a lot of consideration, and with a very heavy heart, I have decided the time is right for me to move on," he told the club's official website http://www.manutd.com.
Faria has been assistant manager at Old Trafford since Mourinho took over two years ago, having first worked with his fellow countryman 17 years ago at the Portuguese club Leiria.
"My heartfelt thanks go to the manager, Jose Mourinho, for the belief he had in me, all those years ago, when it all was just a student dream," he added.
"The intelligent student is now a football expert, ready for a successful career as a manager," Mourinho said.
The pair have one more vital match together, in Saturday's FA Cup final against their old club Chelsea.
But after Sunday's 1-0 win over Watford in their last Premier League game, Mourinho said he would not be appointing a replacement. He added that he thought Michael Carrick, who is joining the coaching staff, would eventually take on the role.
"I have nobody in the world of football to be my assistant. I think it will be Michael Carrick in the future, when he has his badges," Mourinho said.
"When he has his pro licence, when he makes the bridge from player to assistant.
"I got to Michael in the last part of his career and it was enough to fall in love with the player and person."
(Reporting by Steve Tongue, editing by Pritha Sarkar and Toby Davis)
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