Having been in Bayern's reserves only last August, Müller, 20, is enjoying a stellar season having won his first cap in March, helped Bayern reach the Champions League final in April and now begun May with the German title.
Bayern finish the season at Hertha Berlin next Saturday, but after rivals Schalke lost 2-0 to Werder Bremen, Munich will win their 22nd German league title regardless of results as they have a vastly superior goal difference.
"It's a huge weight off our shoulders, because we're there at last," said Müller, who scored his first two goals inside 20 minutes and completed his hat-trick on 69 minutes.
"We've worked for this the whole season. We're proud of the way we pulled together as a team and escaped the alleged crisis situation we were in," he said. "Winning the title is a just reward for the club and the players."
Having already made his Germany debut against Argentina in March, Müller is set to travel to next month's World Cup in South Africa.
He has developed considerably under Bayern coach Louis van Gaal who has won
the Bundesliga in his first season in charge having also picked up La Liga titles with Barcelona and last season's Dutch title with AZ Alkmaar.
"We've hit our most important target, winning the Bundesliga," said van Gaal.
"This trophy means a lot to me. There aren't many coaches in Europe who've been fortunate enough to win the league in three countries. I'm very proud of that. We want to win more trophies now."
Bayern face Werder Bremen in the German Cup final on May 15 then Inter Milan in Madrid for the Champions League title a week later.
For Bayern's ex-Germany goalkeeper Hans-Jörg Butt it was emotional to win his first Bundesliga title.
"Winning my first trophy at the age of 35 is a bit special," he said.
"It's been an unbelievable season with many highs and lows, and a team with fantastic character.
"And then if you personally finish top for the first time, it's just unbelievable."
Bayern defender Philipp Lahm paid tribute to the team ethic, which saw them claw their way up the table after a poor start under van Gaal.
"When you consider that we were eight points off the leaders at one point, it obviously goes down as a great title triumph," said Lahm.
"It was an amazing feeling when the crowd started reacting to the score from Schalke. We wondered what was going on at first, but then we saw the score on the video screens. It was unbelievable."