Louis Gray has played 9 games for the U23s this season.
The Welsh goalkeeper started out at Wrexham before joining the Finch Farm Academy in September 2015, initially on a short-term deal.
He has had a temporary spell with Colwyn Bay, currently in the Evo-Stik North league but has been behind Mateusz Hewelt in the pecking order for Everton's Under-23s this season, featured only in the Checkatrade Trophy against Notts County and Mansfield Town.
"He comes with excellent references and a very good pedigree," Carlisle goalkeeper coach Dan Watson told their club website.
"Having spoken to him I know that he'll fit in well with the dynamics we have with the keepers already at the club, and also within the wider group.
"Louis is really looking forward to the challenge."