The 20-year-old midfielder joins the club from Fortuna Hjorring in her native Denmark, where she played for the last three years in the Elitedivisionen.
A Danish youth international, she has represented her country at U15, U17 and U19 level.
Manager Matt Beard told Liverpoolfc.com: "Sofie is an exciting young talent who we’ve been monitoring for the past six months or so.
"I’m delighted we’ve been able to bring her in during the January window and it’s an area we were looking to strengthen in.
"She’s got terrific experience for such a young player – with more than 100 senior games. We’ve been really impressed with her progress so far and are looking forward to seeing how that continues in the future."
Lundgaard will take No.15 for the Reds and has already trained with her new teammates at The Campus training ground.
She said: "I’m excited, it’s been a pleasure coming here and I’m looking forward to meeting all the girls, getting started and winning some football games.
"I’ve heard a lot of times that this group is a good group and this is a club with ambitions, and I’m looking forward to being a part of it.
"When I spoke with Russ [Fraser] and Matt, I had no doubt that this club was a good option for me."
The Barclays Women's Super League is a challenge that Lundgaard believes her game will be well suited to.
"I’ve heard that every team is a good team and here every one can beat each other – I’m excited about that," she added.
"I’m a powerful player, I like to play football, can also defend, get good possession and make a lot of goals."
Lundgaard becomes the second signing of the January window for LFC Women following the return of former captain Gemma Bonner.