The 38-year-old pledged to bring the "thunder back" to Parkhead and said he would send his players "out to war" for every match at a press conference this morning.
Lennon has been awarded a one-year contract.
Lennon said: "The challenge is to try to unite the support again.
"What I want to bring is the thunder back. I want this place rocking again.
"I want the passion, I want the noise.
"I want the fans to be able to walk to the ground ready for the players to go to war every time they go on the pitch.
"All those things will be in-built before the season starts."
He added: "We've got to put up a really stronger challenge to Rangers and try to wrest the title away from them."
Lennon confirmed Finland coach Stuart Baxter is one of four candidates in contention to come in and work alongside him.
"He's a candidate," Lennon said, amid reports the Finnish FA are reluctant to release Baxter.
The former Celtic captain replaced axed boss Tony Mowbray who departed the club in March following a 4 - 0 humbling to St Mirren.
Following his appointment, Lennon galvanised the squad into achieving eight straight SPL wins.
A semi-final Scottish Cup loss to Ross County proving to be the only black mark on the Irishman's record.
Lennon added: "It's a wonderful moment for me.
"I don't think anyone knows the club better than myself. There are just other aspects I need to work on.
"I think it's a priority to challenge for the title.
"Last season wasn't good enough but the players showed me they have it in them.
"They proved a lot to themselves over the run-in.
"We know we've got to hit the ground running.
"We'll be looking to bring in a few players with experience and a bit more nous."
Celtic chairman John Reid insisted Lennon was always the first choice for the full-time job and denied anyone with authority from the club had approached the likes of Republic of Ireland boss Giovanni Trapattoni.
"We considered, we debated, we maintained dialogue with Neil throughout that," Reid said.
"On every occasion our head brought us back to where our heart had started.
"We came back to Neil Lennon.
"I offer him my congratulations on behalf of this whole club."