City are understood to have paid £200,000 for the 20-year-old, who had a successful medical on Tuesday.
Blindkilde Brown is one of three signings made by Gareth Taylor's side on deadline day, along with Durham forward Poppy Pritchard and defender Tara O'Hanlon from Peamount United
All three players have signed a three-and-a-half-year deal.
Blindkilde Brown is seen as a replacement for the injured Jill Roord, who ruptured her anterior cruciate ligament (ACL) last week.
The England youth international has made more than 50 senior appearances for Carla Ward's side and started eight of Villa's 12 Women's Super League matches this season.
"I'm really excited to be here. It's a big step in my career but I'm really excited to see what comes," Blindkilde Brown said.
"It's a new challenge for me. Obviously, I've been at Villa a lot of my career but it's something new and I'll be training with some of the best players in the world.
"I think the style of play here is really suited to me. Hopefully it just develops me even more in my career."
City are three points off leaders Chelsea and are seeking their first title in eight years.
Villa, who sit eighth in the table after a disappointing start to the campaign, have lost versatile England international Lucy Parker to a long-term ankle injury this year.