Both defenders - regulars this season despite being just 20 and 21 - are now committed to the SPL club until the summer of 2015.
Caley Thistle manager Terry Butcher told the club website: "I am extremely delighted that we have extended Graeme's and Josh's deals.
"They have performed brilliantly for the first team and thoroughly deserve their new contracts.
"This is a fantastic Christmas present for the Club and supporters. I am optimistic that there will be other news of further extensions to other players in the near future."