Caley Thistle confirmed that the players had both tied themselves to the Clydesdale Bank Premier League club until May 2015.
Manager Terry Butcher, whose second-placed side host St Mirren on Boxing Day, told the club website: "I am extremely delighted that we have extended Graeme's and Josh's deals, as 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."
Scotland Under-21 international Shinnie came through the youth ranks and has been an ever-present this season after his development was stalled by a lengthy absence following a serious illness.
Meekings, who is a year younger at 20, has made 44 appearances since signing from Ipswich 18 months ago.
Butcher is still trying to persuade Shinnie's older brother, Andrew, to sign a new contract.