The 30-year-old Norway international has only featured twice for the Whites this season, with both his appearances in the EFL Cup.
Johansen played 36 times for Fulham in 2019-20 as the Craven Cottage outfit were promoted to the Premier League.
He is QPR's third signing of the January transfer window.
"He is a player who has shown he can play in a deeper-lying midfield role or in a more attacking position. That flexibility he has is vital for us."