Tunnicliffe and Larnell Cole have joined Fulham in permanent deals from United.
"I've known Rene since I was nine," Tunnicliffe told Fulham's official website. "I'm here now and glad to sign.
"I want to play at the highest level I possibly can and, to me, that's the Premier League because it's the best league in the world. I want to play as many games as I can and improve as a player because I'm only young. We'll see where we go from there."