The Foxes stepped up efforts to poach the Denmark international from the South Coast after defender Wesley Fofana was ruled out for the rest of the year with a leg injury.
Vestergaard is available for Leicester’s opening Premier League game against Wolverhampton Wanderers on Saturday, having trained with Brendan Rodgers’ men after the two clubs agreed a transfer fee earlier in the week.
The 29-year-old joined Southampton from Bundesliga side Borussia Monchengladbach in the summer of 2018 and made 30 appearances in the Premier League last season, scoring three goals.
Speaking to the club website, Vestergaard said: “I’m very happy and I’m really excited to get going. It’s a special club that has done very well over many years and I think the project is very, very exciting, even from the outside looking in. To be a part of it is a big thing for me.
“I know a couple of the players, and Kasper (Schmeichel) and Ryan (Bertrand) I know very well and get along with off the pitch, so that’s going to be very easy. Just from my first impression of the guys in the dressing room, they’re a good bunch, and I’m sure I’ll settle in very quickly.”
Vestergaard has won 28 caps for the Denmark national team and was part of the side that reached the semi-finals of EURO 2020.
