Cornelius, who would be the promoted side's first signing for the summer, impressed in his first full season in the Danish Superliga, scoring 18 goals in 32 appearances and breaking into the national side.
The 20-year-old will complete the move to south Wales once he has passed his medical.
A statement on the Cardiff website said: "Cardiff City Football Club have today reached an agreement with F.C. Copenhagen for the services of Andreas Cornelius, the 20-year-old striker is set to join the club for an undisclosed fee on completion of his medical."
Although Cardiff are not revealing the fee for Cornelius, the Danish club's website claims it is 65 million Krone, or £7.5million, which would represent a club-record outlay for the Bluebirds.
FC Copenhagen sporting director Carsten V. Jensen told tipsbladet.dk: "It was never the plan to sell Andreas but sometimes a situation arises where it wouldn't be responsible to reject an offer like that.
"We wouldn't normally sell a player so quickly after they've broken through to the first team. The last example of this was when we sold Christian Poulsen after the turn of the millennium.
"But this was a situation where the offer was so big that it would have been irresponsible to turn down. That is how it is."