The 43-year-old had been out of work since he was sacked by the Toffees in December 2019.
Fulham, who will spend next season in the championship following their relegation from the Premier League last term, parted company with Scott Parker earlier this week, with the former England midfielder joining Bournemouth.
Silva has also managed Hull City and Watford in the past but this will be his first time coaching in the second tier. The former Olympiacos boss will be assisted in his new role by Fulham fan favorite Luis Boa Morte.
"I'm really pleased and proud to be appointed head coach of such a historic football club," said Silva after his appointment.
"I want to thank the owner, Mr 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."
Fulham chairman Shahid Khan said: "I met Marco Silva in Portugal last week and was inspired. Marco's body of work in football was evident, but listening to him break down in detail his experiences at each of his stops as a head coach was thoroughly impressive.
"Marco also came prepared, with a full understanding of the players we have and ideas on how we can move forward this season. I loved his energy and optimism, and I'm confident Marco Silva is the right choice to lead Fulham Football Club as our new head coach.
"Finally, Marco will add to his backroom staff a true fan favourite. Luis Boa Morte played here, worked here, knows the club and appreciates what the Fulham badge means to the supporters. That's a plus for all of us."
