Ivory Coast-born centre-back Okore (pictured) has seven caps for the Denmark senior side, but came to the attention of clubs around Europe after starring for the 2012 Danish Superliga winners in this past season's Champions League despite Nordsjælland going straight out after the group stage.
He heads to Villa Park on a four-year contract.
"We're a young team and we played some really good football over the second half of last season which is something we want to build on now as players, as a team and as a club," Okore told the club's official website.
"I know there is great potential in the team. I have watched many of our games because the Premier League is very popular back in Denmark.
"I know also that we have a good coach and this is a really good club. This is the right club for me, I feel it straight away.
"We have a lot to show and we have a long way to go. We want to get to an even higher level of performance and show people who we are, that we can be a really good team."
Villa confirmed earlier this week they are close to signing Danish striker Nicklas Helenius from Aalborg, which will make a double-deal for promising young talent from the Scandinavian nation.
And later on Thursday, the Premier League outfit completed a second deal of the day in the form of 21-year-old Bacuna.
The Dutch under-21 star, of Antillean ancestry, made 109 Eredivisie appearances for Groningen over four seasons and has signed a three-year deal.
"It feels great. It's a new beginning for me, a new step and I'm looking forward to being part of this young, hungry team we have at Villa," Bacuna said.
"This is a dream come true for me and also for my parents who are delighted for me. It's a tremendous league to be a part of, the Premier League, and we want to show that Aston Villa can takes its place among the top teams.
"I'm really excited to come here. Villa Park looks magnificent and the training facilities at Bodymoor Heath are first class. I'm really impressed with the set-up here and I'm proud to be a part of this club."