Cook has scored just one fifty in his last 22 one-day innings for England and he has paid the price for failing to stop the rot during his country's recent 5-2 series defeat in Sri Lanka.
England's selectors are reported to have decided to axe Cook as skipper at a meeting on Friday, with the "Daily Telegraph" saying Eoin Morgan is now set to lead the side for the tri-series in Australia after Christmas and then the World Cup in Australia and New Zealand in February and March.
After England's series-ending defeat in Colombo on Tuesday, Cook, who hasn't scored a one-day century since June 2012, conceded he could have no complaints if he lost the one-day captaincy.
But the decision to remove him from the role with the World Cup looming is still a major reversal by Paul Downton, the managing director of England cricket, and head coach Peter Moores, who have given Cook absolute backing this year.
Cook is expected to be able to continue captaining the Test side and will focus on England's bid to regain the Ashes against Australia next year. Yorkshire's Gary Ballance is believed to be the leading contender to replace Cook in England's 15-man World Cup squad, which will be announced on Saturday, with Moeen Ali and Alex Hales a potential new opening partnership.
The England and Wales Cricket Board had yet to confirm the decision ahead of that squad announcement, but several former England captains were quick to voice their support for the move. "I think it'll be a relief to Alastair," Mike Atherton, who led England in the 1990s, told "Sky Sports News".
"He can now concentrate on batting in Test matches at the top of the order. I don't think Eoin Morgan is going to be in the Test side so he can concentrate on the one-day side of things.
"I think it's the right decision. It makes them look a bit silly, so in many ways a brave one. "Let's face it, England can't do much worse than they have been doing in recent times in one-day cricket."