Opener Cook, who has been woefully out of form with the bat, will be replaced as skipper by swashbuckling middle-order batsman Eoin Morgan.
Cook was at the helm when England lost 5-2 in Sri Lanka in this month's one-day series.
The 29-year-old Essex batsman has toiled all year in the 50-over format, hitting 523 runs in 20 matches at a mediocre average of 27.52
Morgan, however, has fared even worse with the bat in 2014, averaging 25.45.
But the 28-year-old Middlesex left-hander has an impressive record in the eight one-day matches in which he has captained England, piling up 427 runs at an average of 71.16.
England will warm up for the World Cup by playing in a Tri-Series competition in Australia next month that also features India.
The World Cup starts on Feb. 14 and Morgan's men have been drawn in Pool A along with Australia, New Zealand, Sri Lanka, Afghanistan, Bangladesh and Scotland.
RIGHT DECISION
Former England skippers Nasser Hussain and Mike Atherton backed the decision to drop Cook.
"What you can't survive as captain is scoring no runs when the team are losing and that is what's been happening for Alastair in one-day cricket," Hussain told Sky Sports.
"The only way England are going to do well in this World Cup is if their star...Eoin Morgan...finds some form. I think it is the right decision because England need him to fire."
While there is no doubting Cook's pedigree in the longer format, he has hit 8,423 runs in 109 tests at an average of 46.02, his limited strokeplay is not ideally suited to one-day cricket.
"I had grave doubts about Cook's elevation to the one-day captaincy three years ago," said Atherton. "I thought it was the wrong call then.
"I'm sorry they made it that way because we've got to a stage now just before the World Cup where there is a change of captain which is not ideal.
"England can't do much worse than they have been doing in recent times in one-day cricket. So it's a bold move, they've thrown a bit of caution to the wind, they’ll send some young players out there to play with freedom hopefully and see where they go."
(Editing by Toby Davis)
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