The Scotland Under-21 striker spent last season on loan with Falkirk, scoring six goals in 20 appearances.
“I have watched Mark from afar for a while now,” Town boss Paul Sturrock told his club’s official website.
“He had a successful loan spell at Falkirk last season and managed to force himself into the Scotland Under-21 squad.
“He has great talent, he is a big lad and I am hoping that kind of target man will give us an out ball should we need it.”
Beck, 21, lists Carlisle as his only previous permanent club, scoring 10 times in 77 appearances.