Villa announced that 20-year-old centre-back Okore had joined them from FC Nordsjaelland on a four-year contract.
That was swiftly followed by the news that Bacuna's switch from FC Groningen had also been completed, the 21-year-old having put pen-to-paper on a three-year deal.
Okore told www.avfc.co.uk: "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."
With Nordsjaelland, Ivory Coast-born Okore won the Danish cup in 2011 and league title in 2011-12, and featured in the Champions League group stages last term.
He made his debut for the Danish national team in November 2011 and has won seven senior caps.
Of his new club, Okore said: "We have good players all around. It's going to be tough but I really hope I can go in and show myself and be a big part of the team.
"I want to bring something new to our game and really help the team into a new era.
"If I was to describe myself, I think I'm a big, strong defender with good pace.
"Obviously, my priority is to be a really good defensive player but I think I can bring something to our game offensively, too, and maybe start some attacks.
"We have players who have experience of the Premier League and hopefully I can also bring something from my experience in the Champions League."
Villa boss Paul Lambert said: "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.
"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."
Regarding Holland Under-21 international Bacuna, Lambert added: "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."
Bacuna said: "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.
"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.
"The manager is trying to create a new generation, to build something here and make a lot of young guys show what they can do. I'm up for the challenge.
"I'm a player who plays box-to-box, I like to run and I look to shoot."