West Ham boss Sam Allardyce has become frustrated with Morrison, who he feels could have played through his recent groin injury and a move to QPR is now set to happen on Friday, February 21.
QPR have delayed the 93-day loan for the midfielder so that he would be eligible to play in the Championship play-off final if they get there.
The 21-year-old was a key performer for Allardyce earlier in the season, and his form led to England Under-21 recognition, but injuries and a slump in form have seen his first-team chances restricted.
The former Manchester United player has only played three games since the start of the year for West Ham and has not started a game in the Premier League since December.
QPR manager Harry Redknapp revealed his interest in signing Morrison following his side's loss to Derby on Monday night.
Redknapp told Sky Sports News: "If he does want to come and they want to loan him out, we'd be interested, for sure. He's a talent, (and) can open doors and make the difference."