The Daily Mail says their £20mIllion offer for Wilson has been accepted.
Aston Villa - who offered £21m on Saturday - have withdrawn their interest as Newcastle is the player's preferred club.
Wilson will now finalise terms with the Magpies and it is hoped he will complete his move in the coming days.
Newcastle winger Matt Ritchie - who Bournemouth retain an interest in signing - is not part of the deal.
Steve Bruce is desperate for attacking reinforcements and is set to land his top target. The head coach has lost Dwight Gayle to a knee injury until at least December and only Andy Carroll has featured in recent warm-up matches.