The Red Devils assistant, who has worked alongside Mourinho for more than 17 years, intends to take the step into full-time management.
In a statement on United's official website, the 42-year-old said: "After a lot of consideration, and with a very heavy heart, I have decided the time is right for me to move on.
"I have had 17 years of incredible and unforgettable experiences. However, I have felt for some time that I would like to spend much more quality time with my family before pursuing any new challenge in my professional life. 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.
"I would like to thank him for the opportunity and confidence, for the knowledge and experience, but most importantly for his friendship. I would also like to thank Manchester United and all the clubs where I have had the privilege of working during this period.
"I would like to say a big 'thank you' to all the staff and players who, in different ways, have made an important contribution to my growth as a person and as a professional. I wish you all the best for the future, knowing that you will always be my close friends."
Faria arrived at Old Trafford as part of Mourinho's coaching staff in 2016, following previous spells at Chelsea, Porto, Inter Milan and Real Madrid.