The 20-year-old's transfer will be finalised once international clearance is received.
Cardiff agreed a deal with FC Copenhagen last week and the player underwent his medical at the club's Vale of Glamorgan training base on Monday. Cornelius will join up with his new team-mates next week after a short holiday.
"This is a dream come true for me," Cornelius told Cardiff City Player.
"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."
Cornelius added: "It's been a busy few days as I graduated from university back home over the weekend.
"Both school and football are very important to me, so I had to structure my plans in order to achieve in both.
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