The pair have moved from Old Trafford for an undisclosed fee and join the Cottagers on deals until the summer of 2017, with options for a further year.
Both know Rene Meulensteen from his time at Manchester United and Tunnicliffe is looking forward to working with the Fulham head coach again.
The 21-year-old told Fulham's official website: "I've known Rene since I was nine and there was talk when he took over that he was interested in me, so it's just picked up steam this week really and I'm here now and glad to sign.
"Rene didn't have to sell Fulham to me, for a start they're in the Premier League and I want to play at the highest level. I know René and I know he's a great coach so I'm just excited to work for him. Fulham's a great club anyway - they've been in the Premier League for a long time now and I just can't wait to get started.
"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, and we'll see where we go from there."
Tunnicliffe has previously spent time on loan at Peterborough United, Barnsley and Ipswich Town, while 20-year-old Cole came through the club's academy before making his senior debut for United in a League Cup win against Leeds United in 2011.