Queudrue has been training with The Cottagers at their pre-season camp in Austria, whilst Middlesbrough have already signed his replacement in the form of Julio Arca.
The versatile star is now looking to push on and win a place in the French international setup after finalising his switch to Craven Cottage for an undisclosed fee.
"I really enjoyed my time at Boro, but decided that it was time for a new challenge," Queudrue told the club's official website.
"I met with Chris Coleman and was impressed with his ambition for the future at the club.
"He spoke with great passion about what he wanted to achieve long term and I am happy to be part of those plans.
"My ambition is also to play for the national team, so the next seasons are very important for me, and I look forward to playing well for Fulham where I hope I can also further my national team aims."
Coleman is delighted to add Franck to the squad.
Welcoming perhaps his most high profile summer signing after the additions of Gabriel Zakauni, Jimmy Bullard and Bjorn Runstrom, Coleman expressed his delight at landing the Frenchman.
"Franck is a quality defender and one that I have admired for some time," said Coleman.
"He is a gifted player with great skill, and I know that he will make a difference to our back line.
"I am planning for the future here at Fulham and I know that the additions we have made this summer and back in January have increased our chances of long-term success and I am very excited about the future."