The deal between the two sides included the option for a permanent move in the summer.
The 27-year-old English has found limted playing time during the first half of the season.
With Everton signing Morgan Schneiderlin from Manchester United, Cleverley stood little chance for this to change in the rest of the season.
Cleverley joined Everton from Manchester United in summer 2015 and made 30 appearances in his first season under Roberto Martinez, but fell out of favour at Goodison Park under current manager Ronald Koeman.