The Portuguese coach turned down fresh terms from the Cottagers, meaning his five-year tenure in west London will come to an end.
In turn, Silva, 48, has been linked with the Benfica post as they look to replace Jose Mourinho, who is poised to return to Real Madrid.
"To our fans - I asked you, from day one, to always be with us," Silva said. "And that's what you did these past five years. We achieved a lot together.
"My staff and I always felt your support. It will never be forgotten. Fulham will always be in my heart, and sooner or later I will be back at Craven Cottage."
Appointed in 2021, Silva won the Championship in his first season in charge of the club.
He then helped Fulham establish themselves as a stable Premier League side with 10th, 13th and two 11th-place finishes.
Fulham owner Shahid Khan added: "Marco Silva leaves our club with my gratitude and best wishes.
"Fulham and Marco were an excellent fit for five seasons, but change is inevitable in this game, and we’ve accordingly prepared for this moment."