Davies is set to play against Reading this weekend after Boro accepted a bid on Tuesday night.
QPR will pay a substantial initial fee, with further cash linked to appearances and promotion should Rangers reach the Premiership.
As with the likes of Dan Shittu and Arthur Gnohere, Davies has been secured after individual R's fans agreed to stump up the cash to sign him.
Boro initially rejected a £350,000 bid for Davies but by Tuesday morning it was clear Rangers were making progress and were likely to get their man.
Ipswich and Wigan were also interested but Davies made it clear he wanted to return to Loftus Road, where he impressed during a recent loan spell.