The 38-year-old, who has also been registered as a player, terminated his playing contract with Morton on Friday in order to move to Tynecastle.
Combe will coach Jamie MacDonald and Peter Enckelman along with Mark Ridgers, who is out with a knee injury.
Combe told Hearts News: "I'm here to keep things ticking over and keep Jamie progressing.
"He has done extremely well to get where he is but my job is to keep him on his toes and push Peter at this moment in time to try to get the gloves off Jamie.
"And when Mark gets back fit again, we should have all three fighting for that one position.
"I don't want to hang up my gloves yet and feel I have two or three good years left in me.
"I am registered as a player so won't be stopping just as a coach. I'm here as cover if we have any problems but I see myself pushing the guys every day and hopefully that keeps them on their toes."