Rodgers vows to stay with Celtic after fourth successive Scottish title
Nicolas Kuhn and Adam Idah both scored twice after Ryan Strain's own-goal set Celtic on course to wrap up their 13th Scottish crown in the last 14 seasons.
With four matches left for Celtic, the champions sit 18 points clear of second-placed Rangers, who have five games remaining.
The Glasgow club have claimed 21 of the last 26 domestic trophies as Rodgers' men reign supreme in Scotland.
Rodgers has been linked with a move to Leeds, who have won promotion to the English Premier League for next season.
But, with the title secured, he is adamant his future still lies at Parkhead.
"It's been interesting the last few months, people deciding where I was supposed to be going and I wasn't happy," he said.
"But I would say listen to what I say, not what people try to anticipate my mood and what it might be. I said 150, 200 percent I'll be here for sure next season because we want to build again, we want to grow.
"What I'll also say, there's very, very few people that know me and there's even less understand me. Absolutely, I am so, so happy."
Celtic had only needed a point at Tannadice to start their title party, but their goal spree ensured the celebrations went with a swing.
It was a familiar feeling for Celtic after a 5-0 win at Kilmarnock last term earned Rodgers the title in his first season back at Parkhead.
Rodgers' latest triumph moved the former Liverpool manager on to 11 major trophies as Celtic boss.
"My emotional attachment to the club clearly has me here rather than elsewhere. And just the chance to be the best manager at Celtic that I can possibly be. And days like this make it really special," Rodgers said.
"I said minimum I would be here three years. The big thing with Celtic, it's about having the energy. That's the big thing, and there's lots of other things of course."
'Super hungry'
The title success keeps Celtic on course for their sixth treble in nine seasons, and Rodgers' third, when they face Aberdeen in the Scottish Cup final in May.
Celtic substitute James Forrest also wrote himself into the club record books with his 26th winners' medal, one more than Bobby Lennox, who played for the team's famous 1967 European champions.
There was a brief interruption to Celtic's title clincher when visiting fans threw dozens of tangerines -- in reference to Dundee United's nickname -- on the pitch in protest at the home club's ticket prices after they were charged up to £42 ($56).
Despite that hold-up, Celtic's title has been in little doubt since early in the season, with Rangers falling behind early on and Aberdeen collapsing in spectacular fashion after matching the champions' 31 points from the opening 11 games.
The Hoops didn't suffer their first league defeat until January 2 at Rangers, but were still 13 points ahead and a collapse was always out of the question.
Rodgers had criticised his players for being too comfortable after a defeat against bottom club St Johnstone earlier this month.
They have responded in emphatic fashion by hitting five goals in each of their following three matches.
Having also reached the Champions League knockout round play-offs, where they lost narrowly to Bayern Munich, Rodgers will now set his sights on strengthening Celtic for more domestic glory and European drama next season.
"As any manager, you need to feel wanted, you need to feel appreciated. You need to feel that you can develop a team, you can develop a club," he said.
"I'll go into next year super hungry to beat this year, whatever we end up doing."