Caley Thistle confirmed 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."
He continued: "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.
Caley Thistle moved back into second on Saturday with a 4-1 victory over Dundee that saw them equal last season's SPL tally of 42 goals at the halfway mark of this campaign.
The win was watched by 3,003 fans and, although Butcher was pleased with the turnout in torrential conditions on the busiest shopping day of the year, he hopes more supporters come out against St Mirren.
"Our crowd will come because they see the football that we play," Butcher said. "I want them to come and cheer us on all the way because who knows what can happen?
"St Mirren had a good win too and the last time we played them it was 2-2 and goals galore. But there seems to be goals galore every time we play."