The 24-year-old goalkeeper has signed up with the Scottish Premiership club for the remainder of the season.
Kelly, who started his career at Rangers, joined west London club QPR from Livingston in June 2019.
The former Scotland call-up told Well's official website: "I'm grateful for the opportunity Motherwell have offered me. My objective is to play games. I know there's strong competition here and I will have to earn my place.
"I'm ready and available when called upon. We've got a good squad and need to start picking up results."
Kelly will wear the number 13 jersey vacated by Jordan Archer, who has moved to Middlesbrough.
"Liam will strengthen our options in the goalkeeping department, with Jordan Archer having left us," interim manager Keith Lasley said.
"He has already proven his ability at this level, playing a big part in Livingston's success and also earning the recognition of an international call-up."