Fosu-Mensah spent the 2017-18 campaign on loan at Crystal Palace, and made 24 appearances in all competitions for the Eagles before returning to United.
The 20-year-old was involved in United's preparations for the 2018-19 campaign, but has now moved on loan to Fulham for the new season.
"I have a good feeling about the club. It has a nice history, it's a nice club. Fulham has a lot of good players, and it's good for my development to be here," Fosu-Mensah told the club's official website.
"I spoke to the manager and he gave me a good feeling. I'm happy to be here and I want to keep progressing."
Fosu-Mensah, who can play at right-back and in central defence, has been with United since 2014, and has appeared on 21 occasions for their first team.