The 23-year-old is set to complete the move on January 1 and is expected to go straight into the squad for the game against Celtic.
Taylor won a summer move to the League One outfit after netting 29 goals for Falkirk last season, but has found the back of the net just twice so far this term.
Partick boss Alan Archibald said: "I'm delighted to have managed to bring Lyle to Firhill, he will complement the strikers that we already have at the club.
"Things haven't work out for him with United so far which can happen when there is a change in manager, but he carries a potent threat and has a real eye for a goal.
"He's quick and he is good at getting in behind defenders as well.
"I'm sure he will prove to be an important addition to the squad for the second half of the season."