Carroll was on loan at the Hammers this season scoring seven times and Sam Allardyce has constantly expressed his desire to sign the striker on a permanent deal.
The salary for Carroll is understood to be supplemented by a pay off from Liverpool as part of the £15.5m transfer fee.
The Reds paid Newcastle £35m themselves for the 24-year-old in 2011, but he has never quite hit top form at the Anfield club, where he has scored 11 goals in 58 appearances.
The 6ft 3in striker has also made nine England appearances and recently forced his way into Roy Hodgson's squad for friendlies against the Republic of Ireland and Brazil before withdrawing due to a heel injury.
Hammers manager Sam Allardyce wants an answer from the striker regarding the deal this week before Carroll returns from his holiday.
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