Aaron Hughes, Steven Davis and Chris Baird have all moved to Craven Cottage during the close season.
Healy, Northern Ireland's record goalscorer, has agreed a four-year deal with the London club.
"David has showcased his striking pedigree at the highest level with Northern Ireland in recent years, and I have every confidence that he will produce the same form for Fulham," said Sanchez.
The 27-year-old striker has scored of 29 goals in 59 appearances for his country. "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 am really looking forward to playing under him in the Premier League," said Healy.