The former Macclesfield player has accepted a one-year contract extension after impressing in midfield for Caley Thistle.
The 24-year-old expected to be fighting a relegation battle when he arrived last summer but Inverness are in third place in the Clydesdale Bank Premier League ahead of the clash with Dundee at Dens Park.
And he wants to make sure that their exploits this season are not a flash in the pan.
Draper, whose team-mate Billy McKay signed until May 2015 on Thursday, said: "It's been ongoing for a while; it's always been close to being done, apart from signing it's a done deal. I've enjoyed my time here so I'm looking forward to next year.
"It's important for the team that we keep the majority of the players together and build on this year.
"We don't want it to be a one-off year where we finish in the top six and then next year we are struggling again. We want to kick on and turn the club into a solid top-six team."