The 20-year-old centre-back underwent a medical on Thursday before penning a deal that will keep him at the club until 2017.
Okore, who has moved for a fee believed to be in the region of £4 million, finished as a runner-up in Denmark's Superliga last season, and featured five times for Nordsjaelland in the Champions League.
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"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.
"I'm really excited and I'm looking forward to seeing my new team-mates and getting together with them to train and get prepared to play some Premier League games."
Villa manager Paul Lambert is delighted to have secured the signing of Okore, and believes he brings depth and quality to his side.
"He's only 20 years of age and that's good but he's also an international player at a really young age and he's played Champions League football as well, which is testament to his potential," Lambert said.
"Jores has played in big games but he's a very humble lad and he will be a really good addition to our team and to our squad. I'm pleased that we've signed a player of his stature, for he is someone who can come in and make a huge impact.
"There's a great opportunity for him here and the competition for places is something that's really important. You want to try to have that throughout the team."
The Villa Park outfit have moved quickly in the transfer market this summer, already securing the services of Bulgarian winger Aleksander Tonev, tying Andreas Weimann down to a new three-year contract and they also hope to conclude a deal for Nicklas Helenius in the coming days.