Both players have signed contracts that run until 2017 with the option of a further year and will once again work under Cottagers manager Rene Meulensteen, who was part of the Red Devils' coaching staff from 2007 until 2013.
"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."
Fulham are currently second from bottom in the Premier League with 19 points from 23 matches.