Silverwood had come under pressure after England lost the five-test Ashes series 4-0, with former skipper Mike Atherton calling for a complete overhaul of the England management.
The announcement comes a day after Ashley Giles left his role as the managing director.
"It's been an absolute honour to be England head coach, and I'm extremely proud to have worked alongside our players and staff," Silverwood said.
"The last two years have been very demanding but I have really enjoyed my time with the team and working with Rooty (test captain Joe Root) and Morgs (white-ball skipper Eoin Morgan), and I am very proud of this group considering the challenges."
"In the coming days Andrew Strauss will appoint a caretaker coach for the tour of the West Indies and will then consider the appropriate coaching structures to help England move forwards," ECB chief executive Tom Harrison said in a statement.
England have reinvented themselves as a white-ball powerhouse since their early exit from the 2015 World Cup, winning the next edition of one-day cricket's biggest title on home soil.
But their record in the longest format of the game has been less impressive in recent years, with the final Ashes test loss in Hobart marking their 15th consecutive test in Australia without a win.
Root's future as the test skipper has also come under doubt after the humiliating Ashes capitulation to Australia. All-rounder Ben Stokes is considered a viable option to replace him.
British media reported that batting coach Graham Thorpe could also be relieved of his duties after a series of batting collapses by the team in Australia.
Following Silverwood's exit, England are now on the hunt for their third head coach since 2019.
Justin Langer has been linked with the England role and could soon be available after being told by Cricket Australia that he would have to reapply for the job at the end of his contract.
England are due to play three test matches against the West Indies starting from March 8 in North Sound, Antigua. Last month, they lost the Twenty20 series 3-2.
