The former Hull City, Watford and Everton manager has signed a three-year deal at Craven Cottage.
Silva has been out of work since being sacked by Everton in 2019.
Fulham said on their official website: "The club is delighted to announce the appointment of Marco Silva as our new head coach.
"Silva has agreed a three-year deal with Fulham, keeping him at Craven Cottage until the end of the 2023/24 campaign.
"He will be assisted by club legend Luis Boa Morte, who made 250 appearances in a six-and-a-half year spell."
Fulham were relegated last season after one season back in the Premier League, while Silva has been out of work since being sacked by Everton in December 2019.
Silva told Fulham's official website: "I'm really pleased and proud to be appointed head coach of such a historic football club.
"I want to thank the owner, Mr (Shahid) Khan, Tony Khan and the entire football structure of Fulham Football Club for the trust shown in us.
"I'm excited to get started and my message for our fans ahead of this big challenge is we will all be working very hard together to be successful so they can feel proud at the end of the season."
Additional reporting by PA.