Chong was reportedly offered lucrative contracts by both Italian giants, and it was anticipated that he could leave the club for free in the summer.
However, Manchester United confirmed on Monday evening that the winger has put pen to paper on a new two year deal, with the option to extend his stay for a further year.
Chong joined Manchester United from Feyenoord in 2016, and has gone on to feature seven times for Ole Gunnar Solskjaer's side this season, predominantly in the Europa League.
Speaking to the Manchester United website, Chong said:
"I am working hard every day to improve and I know this is the perfect environment to develop my game.
“The opportunity to learn from the manager, his coaching staff and the world-class players here is fantastic. I am delighted to sign this new contract and really grateful for the chance to prove myself here for many years to come.”
The Netherlands Under-21 international is held in high regard at Old Trafford, and made his debut for United under Solskjaer, coming off the bench during their 2-0 FA Cup victory over Reading in January 2018.
Chong was one of a handful of young players thrown by Solskjaer during United's famous 3-1 victory over PSG in the Champions League second leg, as the Red Devils completed a stunning comeback to progress into the quarter finals.
The youngster entered the fray in the 80th minute, with fellow teenager Mason Greenwood also joining him on the