The 18-year old, currently on loan with First Division club Cowdenbeath, has penned a two-year deal with the Fir Park outfit.
Moore is yet to make an appearance for the Well first team but is highly rated by the club and was thrilled to pen a contract extension.
"I am pleased with how this this season has gone so far, and signing this contact is the icing on the cake," he told the club's official website.
"I really enjoyed playing for Jonathan Johansson with the Under 20s and although the results weren't going for us, I could feel the benefit of coming up against some experienced opponents.
"Going on loan has also proved a great experience; I enjoy competitive football with Cowdenbeath every weekend.
"With my future sorted, I am looking forward to the next few years. I will work as hard as I can to try and win a spot in the first-team squad then we'll take it from there."