Silva's tenure as Toffees manager will begin with a trip to Wolverhampton Wanderers on the first weekend of the season, before hosting Southampton and travelling to Bournemouth in their next two.
The Merseyside club will then face Huddersfield Town (H) and West Ham United (H) ahead of a trip to Arsenal on September 22.
Campbell has backed his former side to get off to a strong start as they look to improve on last season's eighth-placed finish in the Premier League.
Campbell told Sky Sports News: "They are a great first six fixtures to put the club on a good standing. I think they are very, very good fixtures for Everton to start the season."
Everton won 13, drew 10 and lost 15 of their 38 Premier League matches last season.