The 24-year-old has been signed to cover for the loss of Johnny Russell, who is out for the remainder of the campaign after suffering a broken leg.
Boulding played for Mansfield, Bradford and Accrington Stanley before signing for Livingston, scoring 12 goals in 29 games last season.
He was snapped up by Kilmarnock on a three-year contract in the summer, but he made only four appearances - three as substitute - before his contract was terminated in January.
Dundee United manager Jackie McNamara said: "With Johnny Russell's injury, we are short on forwards and when I heard Rory was available I moved quickly to bring him in for a trial.
"He has shown me he can offer us something with his energetic and busy style so I am delighted to have him sign a contract. He is fit enough to be considered for action immediately and I think he is someone the United fans will quickly grow to enjoy."
Boulding added: "After being offered the chance to come in and show my worth here, I am delighted to sign this contract which gives me a further opportunity to win a longer term deal at the Club.
"The ability within this squad is excellent and I want to be part of that. The Manager has a vision of how he wants to take this Club forward and to be offered the chance to be involved is something I am looking forward to."