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The move is subject to the 24-year-old agreeing to the move and agreeing personal terms.
Carroll spent this season on loan from Liverpool, who paid Newcastle £35 million for him in January, 2011.
West Ham also announced on Tuesday that they have signed Romania captain Razvan Rat on a free transfer.
The 31-year-old left back was out of contract after a decade with Shakhtar Donetsk in Ukraine.
"I'm hugely happy that we've got a player of his experience and his character," West Ham manager Sam Allardyce said.
"He's been playing Champions League football this year and at the highest level for many years. Shakhtar had offered him a very good contract, but his ambition was to come and try his abilities and skills in England.
"When you hear somebody speak so positively about that, then you know they've got the mental character that's needed to do well in this division.
"We certainly know he's got the ability and he's at an age where he's still capable of producing at 31."
