The 22-year-old has agreed terms on a three-year deal and will become Paul Groves' first signing later this week.
A Northern Ireland international, McQuoid originally joined Millwall on loan in January 2011 after making 69 appearances for the Cherries. A permanent move to The Den followed, but the forward failed to break into the first team and was sent on loan to Burnley.
Bournemouth boss Groves told the club's official website: "I'm delighted and I think it's a good bit of business for the club. Josh gives us a variety of options and he will enhance the group.
"He can play out wide or up front and gives us versatility. He has international experience, adds energy and he's got a good goalscoring record, so he brings a lot to the squad.
"He knows the club and he's from the area. It's great that he has decided to commit to us for three years and wants to be part of what we are trying to achieve."