Kane, 30, swapped boyhood club Tottenham for the Allianz Arena in a deal that could be worth £100million.
He had been linked with a move away from Spurs for the past few summers, including while heading into tournaments as England skipper.
Now Kane’s future has been sorted, during a year where England were not relying on his goals, Southgate is pleased to see him hit the ground running at Bayern.
“I definitely think from a selfish England perspective it’s good that his future’s settled now for the next few years,” the England manager said.
“I think potentially that can be a distraction for players. But also it’s good for him that he’s got to go and perform at a new club now. He’s been at one club for so long.
“To have a change means you’ve got to impress new team-mates, new staff, new fans and also there’s the life experience of having the breadth of adjusting to a new country. I think there’s a lot of positives there.”
As England and Tottenham’s all-time leading goalscorer, Kane has already hit three goals in his first two Bundesliga appearances and will be aiming to win trophies this season to break his duck.
He lost two League Cup finals and the 2019 Champions League final at Tottenham but, with Bayern having won the last 11 Bundesliga titles, Kane could finally get his hands on a winners’ medal.
“I’m sure for his own belief that would be brilliant,” Southgate added.
“I’m not sure that he’s going to become a better player but there might be other aspects of the mentality that this move will help him with.
“They’re probably the bits that as you get older are the only bits you can improve upon.
“I think the Bundesliga is a bit different to some of the other leagues we’ve talked about, a bit more transitional.
“There is an intensity to that. We’ll have all the data on that from training sessions and matches, so we’re able to track that really closely.
“I think the big difference for Harry this year will be that there’s going to be a lot of games where they’re very dominant and in the opposition third of the pitch, so I think there will be a lot more play for him in penalty box I suspect than he had in the last couple of seasons.”