The deal was finalised after Cornelius, 20, passed his medical on Monday.
The 20-year-old talisman, who bagged 20 goals in 44 competitive appearances for Løverne last season, will join his new mates and club colleagues next week.
“This is a dream come true for me,” Cornelius told the club’s official website. “I’ve been given a great opportunity and this is a very exciting project that’s taking place at Cardiff City.
“I’m very happy to be here and to be playing for this club in the Premier League.
“There were opportunities for me this summer and I had to think about what was the right thing to do, the correct step for me to take in terms of my career.
“I was impressed by what the club is trying to do, the fact it has reached the Premier League and that it has a passionate fan base supporting it.”
In all likelihood, Cornelius — referred to as the ‘new Nicklas Bendtner’ — will lead the attacking line for Cardiff next season.
Additionally, newly promoted Cardiff City are after the signature of Blackpool F.C. ace Tom Ince, who is also reportedly attracting interest from Liverpool — his former club — and Swansea City.
Blackpool have already accepted the Bluebirds‘ “massive” offer for the England Under-21 international, but Ince has yet to decide his long-term future.
The chances of Ince leaving Bloomfield Road this summer are “50-50,” as revealed by Blackpool boss Paul Ince, Tom’s father.
Ince, 21, tallied 18 goals and 14 assists in 44 league appearances for the Tangerines last term.
Spurs want Halilovic and Jedvaj
Prva HNL powerhouse GNK Dinamo Zagreb have confirmed they are in talks with Tottenham Hotspur about highly-rated starlets Alen Halilovic and Tin Jedvaj, Sky Sports can reveal.
Halilovic and Jedvaj, both 17, are reportedly attracting interest from a number of top European clubs and would reportedly cost Spurs £17.3 million.
The dynamic Dinamo duo are undoubtedly two of the brightest prospects in European football.
Halilovic, who netted two goals in 21 first-team appearances for Zagreb last season, made his senior debut for Croatia eight days prior to his 17th birthday in a friendly against Portugal on 10 June.
Jedvaj scored one goal in 13 league appearances for the 1. HNL champions in 2012/13, but has yet to make his international debut for the Croatian senior team.
“Discussions and negotiations with Tottenham are still ongoing, but this job is absolutely not done,” said Zagreb president Mirko Barisic.
“And Tottenham is not the only one interested, but we hope that transfer will be realised and that Tin and Alen will go to Tottenham, but no-one can guarantee that.
“If the business was done, we would say so and if the transfer is completed, they will both stay at Dinamo.
“I can also reveal that there are many clubs after both of them, there is not a club from the top 20 in Europe that didn’t ask us about them.”