The duo would have been free agents this summer but new Caley Thistle boss John Hughes has moved quickly to secure their services until May 2016.
He said: "I've been impressed by the skill and attitude shown by both lads and feel there is more to come yet from Danny and Carl as they continue to adjust to this level.
"I'm pleased they have committed themselves to being part of this club's future."
Meanwhile, Toby Agdestein left the club on January 7 after his current contract expired.
Hughes told the club's website: "Toby has been a bit unfortunate in the amount of game time he got during his spell with the club but we wish him well for the future wherever that may take him.
"We are working hard to get a couple of additions to the squad during the window and we will see where that takes us, but our main priority remains to secure our current squad members."