The Portuguese, 39, replaced Mike Phelan in January on a deal until the end of the season but could not save them from the drop to the Championship.
He led Hull to six wins from his 18 Premier League games, with relegation confirmed after a 4-0 defeat by Crystal Palace on 14 May.
In a statement, Hull said they were "disappointed" by the departure of a "firm fans' favourite".
The club were relegated in the penultimate week of the season and Silva said at the time: "It's my goal as a manager to work in the Premier League."
The former Sporting Lisbon and Olympiakos manager has been linked with Watford after the dismissal of Walter Mazzarri, but said recently he had not received an offer from the Hornets or any other club.
"Everyone knows when you have the chance to work in the Premier League, you don't want to work in Championship, it's normal," he said last week.
A statement from Hull said Silva "will be forever remembered for his efforts to maintain our Premier League status".
It added: "Unfortunately, after considering his future, he has chosen to leave in order to further his career."
Assistant head coach Joao Pedro Sousa, first team coach Goncalo Pedro and goalkeeping coach Hugo Oliveira have also left the club.
BBC Radio Humberside sports editor Matt Dean:
Marco Silva is undoubtedly a loss, although his departure isn't exactly a surprise. His drive, energy and focus for the job was unwavering and his values rubbed off on his players and the fans. He was always viewed as a coach bound for bigger things and brighter times.
The club will be hard pressed to find another in his mould. Whoever gets the job will have to pick up the pieces of a squad shorn of six loan players now back with their parent clubs and be capable of galvanising those left, including the fans. There are no guarantees either that players such as Harry Maguire, Andy Robertson and Abel Hernandez will remain at the club.
Fans will watch with keen interest to see how serious the club's owners are to get the club back to the Premier League with the next appointment and the resources allocated to them.
Marco Silva has resigned as Hull City manager after the club's relegation.