After leading Hibs to the Championship title last season in his first campaign in charge, the former Celtic manager’s ambitions remain high back in the top flight.
Aberdeen have set the benchmark for the rest of the clubs looking to halt Celtic’s dominance but Lennon wants Hibs to be recognised as the best of the rest.
Lennon, whose team travel to play third-placed St Johnstone on Saturday, said: “I’m delighted to get the contract sorted.
“It gives me incentives and targets to work on now, and hopefully a bit of stability for the club. I hope the fans are as pleased as I am, I’m not too sure the players are! I’ve got a target that I want to make Hibs a big club, a big force in Scottish football.
“I’m enjoying the challenge that lies ahead, the infrastructure is great, the players have been brilliant in everything we’ve asked them.”
Asked how he defined success, the Northern Irishman replied: “Trophies, hopefully results, league finishes.
“I want to be up there, or try to be up there with Aberdeen and Rangers. I think most of the clubs are still way behind Celtic but if we can get into that second bracket then I think that would be suitable for a club of this size.
“It might take a bit of time but hopefully over the three years we can achieve that and be consistent at doing it.”
With Aberdeen looking strong under Derek McInnes, Rangers continuing to build and Hearts hopeful of reviving their onfield fortunes, Lennon believes there is genuine excitement regarding the competition among some of the league’s heavyweights.
He added: “I can’t talk for other clubs but that’s the ambition for this club. I think the Scottish league is sexier now. Rangers are getting strong again and we’re back so there are some big games and big clubs going along
Commenting on Lennon’s new contract, Hibs chief executive Leeann Dempster said: “We are delighted that Neil wants to commit to the club. He is an ambitious guy, he wants to win silverware, and he brings that mentality with him. We look forward to working together to bring supporters more of the success they have enjoyed over the past two seasons.”