The news comes on the same day it has been announced Dan Connor has been forced to quit professional football due to injury.
Cornell, a Wales Under-21 international, has progressed through the youth ranks at the Liberty Stadium and goes straight into the Bulls squad for Saturday's trip to AFC Wimbledon.
United's number one Adam Bartlett has this week been ruled out for the short-term with a thigh strain, an injury which forced assistant manager and registered keeper Russell Hoult to take his place between the sticks in midweek.
Connor's retirement was confirmed due to an ongoing hip problem.
The stopper was signed last summer but suffered a freak injury when stepping out of his car and failed to play at all in 2010/11. The injury has also curtailed his involvement this season and he has now been forced to hang up his gloves on medical grounds.