Cricket Scotland made the announcement on Thursday morning that the Grange is so badly affected by flooding following the welter of rain this summer that they could not guarantee the venue would be ready to stage the match on August 12.
Cricket Scotland chief executive Roddy Smith said: "This is a hugely frustrating decision that we have had to make, but we could not justifiably take the risk of building the facility on a ground so saturated from more than six weeks of rain."
A third of the playing area is under water, five feet deep in places, and 40 metres of the main wall around the ground has been destroyed by the flooding.
The hosts and the England and Wales Cricket Board explored options to move the fixture, but concluded that would not be possible either.
Smith added: "We have been faced with an unprecedented and sustained period of rain that has, unfortunately, taken the season's biggest game from us.
"All ticket-holders will be refunded in full by our ticketing partner, Ticket Soup, and we will be contacting everyone who has purchased a ticket with free offers to attend matches next season. Everyone is very disappointed but understands the exceptional circumstances we are faced with."
ECB chief executive David Collier added: "We share Cricket Scotland's disappointment that the flooding has forced the ODI to be cancelled this year.
"Cricket Scotland has made great progress in recent years, and the ODIs between Scotland and England provide a wonderful opportunity to promote the game and to bring new supporters to cricket.
"We look forward to returning to Scotland in future years and wish our friends at Cricket Scotland every success in the future."