The 20-year-old, at Bayern since 2012, spent last season on loan at Schalke 04 where he made 23 league appearances to help them to a fifth-place finish.
He also spent the second half of the 2014-15 season on loan with Bundesliga rivals Augsburg.
"I’m very pleased. It’s a big opportunity for me. I look forward to giving what I have and what I can to the club. They have put trust in me and I want to show them that they are not wrong," he told the website.
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"When I heard that Southampton came in for me I said to my people that this is what I want to do because I can see myself at Southampton, as it’s the way I like to think, the way I like to play and it fits me really well."
Hojbjerg will become the second arrival at Southampton during the close season after the signing of England under-21 winger Nathan Redmond from relegated Norwich City last month.
Frenchman Puel was appointed Southampton manager on June 30 after Ronald Koeman joined Everton.
Southampton earlier announced the departure of Italian international striker Graziano Pelle to China's Shandong Luneng.
(Reporting by Ian Rodricks/Alan Baldwin; Editing by Keith Weir/Rex Gowar)
