The Netherlands global spent last season on loan at Crystal Palace, where he made 21 appearances in all competitions.
The 71-year-old former England national coach was hired by Palace in September last year, replacing Frank de Boer after the club lost their four opening games without scoring a goal, and, despite losing the next three matches, eventually guided them to 11th place. Newly promoted Fulham beat competition from Bundesliga side Hertha Berlin for his services, sources told ESPN FC.
"We are looking to build on the hard work and results achieved last season and I believe this is the most important part of making that happen".
The Netherlands worldwide, who has made 21 senior appearances for United since his debut under Louis van Gaal in 2016, played 24 games for Palace last season.
There will be plenty of debuts for Fulham, who brought in 12 players during the summer.
Rico, 24, won the Europa League twice with Sevilla and made over La Liga 100 starts for the Spanish club.
Fulham goalkeeper Fabri is set to win the race to start the season as Slavisa Jokanovic's No 1.
A Premier League club has officially announced the signing of two FC Barcelona stars.
And it has been claimed that he is closing in on linking up with Fulham on season-long loan deal as he looks to play more senior football this summer.