The 22-year-old forward came through the ranks at Dean Court before moving to Millwall 18 months ago.
His move to the Championship did not go to plan, though, and McQuoid spent the final three months of the season under the tutelage of former Cherries boss Eddie Howe at Burnley.
"I hadn't played much at Millwall and I went to Burnley where I was in and out of the team, so I wanted to come here and play games," said McQuoid, who agreed a three-year deal on Tuesday as Scott Malone moved in the opposite direction.
"This is where I'm from, but that wasn't the main factor. I spoke to the management team and it seemed like a club that wanted to go far and I wanted to be part of that.
"I think I will settle in quickly because I know a few of the lads already and it feels like home for me here."