Okore arrives from FC Nordsjaelland, last season's runners-up in Denmark's top-flight Superliga, and has signed a four-year-deal at Villa Park.
Bacuna, meanwhile, joins Paul Lambert's side from Dutch outfit FC Groningen on a three-year contract.
The 21-year-old made over 100 appearances for the Dutch side since his debut in 2009, netting five times this season.
Denmark international Okore, who made five appearances in last season's UEFA Champions League campaign, is delighted to be part of Lambert's side.
"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," the 20-year-old said.
"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.
"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.
"I'm happy to be wearing the shirt and I feel like I'm looking really good in it - it feels very comfortable. I'm looking forward to us going out next season, performing as a team and showing our potential.
"We have players who have experience of the Premier League and hopefully I can also bring something from my experience in the Champions League. I'm looking forward to playing with my new team-mates."
Lambert is confident both young players can make a valuable contribution to his Villa side.
"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," he said.
"Leandro's energy and versatility will be really good for us. He's a good player, he has bags of energy and he will make an impact.
"He's another player we believe will do well for us. He has played in big games and he has lots of experience for a player so young."
And Bacuna added: "It feels great. It's a new beginning for me and I'm looking forward to being part of this young, hungry team we have at Villa."