The 27-year-old right-back has agreed a three-year contract at the Premier League club, who hold an option for a further 12 months.
Mbabu, who has 22 caps for his country and previously had stints with Newcastle and Rangers, is initially targeting Premier League survival following Fulham’s promotion as Championship winners.
“I’m happy to be here as a Fulham Football Club player,” he told FFCtv. “It’s a relief and now I can focus on my goals and the club’s goals, and help the team to be successful.
“The first step is to stay in the Premier League, stay stable in the league, and then why not aim for the top 10?”
Mbabu is the fourth summer signing for Fulham boss Marco Silva following the arrivals of Joao Palhinha, Andreas Pereira and Manor Solomon.
Fulham owner Tony Khan said: “Kevin is a player whom we’ve pursued for several years.
“He brings great physical tools to our club in addition to his vast experience, and he’s determined to prove himself in the Premier League.”