Sanchez told the club's official website: "My interest in signing David Healy has been well documented in recent months and I am delighted that he has signed for the club today.
"David has showcased his striking pedigree at the highest level with Northern Ireland in recent years, and I have every confidence that he will replicate the same form for Fulham in the Premiership.
The 27-year-old Northern Ireland international added: "I knew of the manager's interest in bringing me to Fulham at the beginning of the summer and I'm glad, finally, to put pen to paper.
"Obviously I know Lawrie Sanchez well and through his time as manager of Northern Ireland he has given me a lot of support, so I'm really looking forward to playing under him in the Premiership.
"It was a disappointing end to my time at Leeds with the club being relegated and I wish them well for the future.
"But I'm looking forward to joining the other lads that I know from the Northern Irish set-up and, of course, the lads already here and I'm really excited about the future."