The 48-year-old's departure had been widely anticipated following reports that he was close to agreeing a deal with Benfica, who are seeking a replacement for José Mourinho after the Portuguese manager left Lisbon to become Real Madrid's head coach.
In a farewell message addressed to Fulham's supporters, Silva wrote: "After five years, our journey together comes to an end. To our fans — I asked you, from day one, to always be with us. 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."
Silva joined Fulham in July 2021 when the club had just been relegated from the Premier League. He won the Championship at the first attempt and steered the west London club to 13th, 10th, 13th and 11th-place finishes across his four top-flight seasons. A victory on the final day of this season against Newcastle United secured 11th place on 52 points.
Fulham owner Shahid Khan paid tribute to the outgoing manager while signalling the club's intent to move quickly on his replacement.
"Marco and Fulham were an excellent fit," Khan said. "Change is inevitable in this game, and we've accordingly prepared for this moment. The talent in our squad, our historic home ground of Craven Cottage, our faithful supporters, and my commitment to backing the club, all make Fulham an extraordinarily attractive destination for an incoming head coach."
Discussions between Silva and Benfica are understood to have progressed significantly in recent days, with an agreement within reach.