24-year-old Hojbjerg had just one year left on his deal at St Mary's and was stripped of the captaincy by Saints boss Ralph Hasenhuttl in May after publicly stating his desire to move to a bigger club.
The Denmark international has now got his wish with Spurs beating off interest from Ajax and Everton to secure their first signing of the transfer window. The club confirmed the news in a statement published on their website.
Hojberg made 134 appearances in all competitions for the Saints after signing from Bayern Munich back in 2016, picking up an EFL Cup runners up medal in 2017. The transfer fee is reportedly £15m - though this could increase in the future thanks to various add-ons included in the deal.
Hojbjerg's arrival coincides with Walker-Peters' Spurs departure. The 23-year-old spent the second half of the season on loan at Southampton with the south coast making the move permanent for £12m.
Walker-Peters' departure could lead to Spurs delving into the transfer window for defensive reinforcements - particularly if Serge Aurier leaves as well. The Ivorian is attracting interest from Serie A upstarts Milan as well as several clubs in France.
Southampton manager Ralph Hasenhüttl said on the signing of Walker-Peters: "It was not easy for Kyle when he arrived here. He needed some time to adapt to our style of play, and then we had this period where we could not be together as a team.
"But you could see from how he performed when we came back that he had worked a lot in this time, both on his physical condition and also on his understanding of our own game. It says a lot to me about this player that he was able to do this.
"He is a very good fit for our style. He is a young, intelligent player, and he is very good on the ball, with good quickness and an ability to play this intense style that we like. I am very pleased we have been able to bring him back as our player, as this is a position that we have been looking to improve in and Kyle does this for us. I think he can develop his game even more here too."
Kyle Walker-Peters said: “I’m delighted to have signed here. The last few months on loan have been great for me and a lot of fun too. I’ve really enjoyed my football, the atmosphere here and also the style of play.
"The club definitely fits the way I like to play, and I hope that people were able to see that during the last month or so of the season. I feel like I’ve already developed in the time I’ve been here, and that’s a big part of wanting to stay too. Obviously, it’s a club with a great reputation for improving young players and, personally, I’ve found it really valuable working under the manager, with his ideas on the game and what he expects from you as an individual.
“I think the way we finished the season gives us real optimism about where we’re heading too, and it just feels like a really good place for me to keep developing as a player and make the best out of what I have.”