Chelsea, Manchester City, Arsenal and Spurs were all reportedly interested in the promising midfielder but The Hammers look to have convinced Poyet to sign.
He took to Twitter to suggest that he was set to be unveiled as a West Ham player after reports had already suggested that he had completed a medical at the club.
Not ignoring everyone, crazy but exciting last few days. All will be revealed in time. Thanks for the messages #COYI— Diego Poyet (@diegopoyet7) July 5, 2014
The tweet said "Not ignoring everyone, crazy but exciting last few days. All will be revealed in time. Thanks for the messages #COYI" with the "COYI" meaning 'come on you Irons' - a hashtag used by West Ham fans and the club itself.
After breaking into the Charlton first-team in January, Poyet went on to make 23 appearances as The Addicks managed to avoid relegation, and the young star was named Charlton Player of the Year.
His decision to leave the club will have upset Reds fans, and a move to London rivals West Ham will only anger the Championship club more.
Poyet will be Sam Allardyce's fourth summer signing already following the arrivals of Mauro Zarate, Cheikhou Kayoute and Aaron Cresswell.
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