The 20-year-old Bulgarian is yet to make a first-team appearance for Wanderers, but has been a regular for the Under-21 side.
"We've seen Georg and he is very good in the air and has good presence," Carlisle United manager Keith Curle said on the club's official website.
"He has a strong physique and he works very hard off the ball. Andy Hughes, the Under-21 coach at Bolton, speaks very highly of him and we think he'll fit in very well here."
Iliev was called up to the Bulgaria Under-21 squad earlier this month.