Ian Hendon, currently West Ham's Under 21s coach, will step up to replace Downes, and his position will be filled by Nick Hancock, head of the Under 18s, until the end of the season.
Allardyce's relationship with Downes appeared strong as the two celebrated ecstatically during the 3-1 win over Chelsea earlier this month. But the West Ham manager said yesterday: "I can confirm he has left, by mutual consent.
"At the moment that's all I'm prepared to say on the matter because I don't think I need to go any farther publicly. That's done between me and Wally.
"He's sorting out his terms and agreements with the club. That isn't sorted yet. It was amicable between the pair of us and we move on."
Asked if he was the one who took the decision Allardyce said: "I did, yes".