The move will see McQuoid join the Lions on a permanent basis in January.
The Echo understands McQuoid will sign a £4,000 per week three-and-a-half year deal at the Den when the transfer window re-opens in January.
Chairman Eddie Mitchell told the Echo the South London club came in with an improved offer late on Wednesday evening after previously having two bids for the Northern Ireland international rejected.
Mitchell said boss Eddie Howe had tried to persuade McQuoid to remain at Dean Court, but the 20-year-old was adamant he wanted to link up with the Lions.
Rumours suggest Cherries could be in line for around £550,000 from the sale, although Mitchell described the fee as "modest for a young, up-and-coming player" when asked by the Echo earlier today.
McQuoid's departure will be a bitter pill to swallow after Mitchell was quoted in the Bournemouth Evening Echo as saying just yesterday: "When they first made contact, we told them Josh was not for sale. But they made a bid anyway and it was rejected. They came back with another offer this morning which wasn't accepted either. osh is a key member of our squad and we are not looking to disband it. I wouldn't see any great benefit in him going. He is firing on all cylinders for us and we want to keep it that way. believe we are good enough to make the play-offs or better and what would be the point in us jeopardising the bigger prize at this stage in the season".