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 Scottish Premier League ahead of Saturday's 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 yesterday, 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."
Draper has formed an impressive partnership with Owain Tudur Jones and the success of his switch from England's lower leagues has surprised the midfield man.
"It's a great dressing room and a great little club and they do so well to get players up with the part of the country that we are in," he said.
"With players signing on it's really important for the club and hopefully we can kick on and secure that top-six place.
"I've always said I was coming up here for a scrap and a relegation battle, but within a couple of weeks you can tell the quality in the squad.
"I didn't know a great deal about Scottish football but you can tell the players are technically gifted and I believe we have a real chance to do something.
"We've proved teams wrong and pundits wrong so we'll just keep doing our own business, what will be, will be."
The central midfielder is going into the weekend's SPL match with bottom side Dundee hopeful of winning three points that will all but guarantee the Caley Jags a top-six finish.
However, the Englishman knows it will not be an easy game with the Dens Park side fighting for survival.
"They are still a good side - they showed that with a good result against St Mirren (2-1 home win on Wednesday)," he said. "They haven't given up hope and that win will give them confidence to try to get a couple of results before the split.
"It won't be an easy game. We've got to go down there with a winning mentality because we've got the chance to open up a little bit of a gap and, with a win, more or less secure a top-six finish, which has been our aim.
"We are concentrating on ourselves; it's about us and what we can do on the pitch. If we've got the belief that we can play well, do the right things and treat the game with the right respect then most weeks we will get the result which we deserve."