Cornelius, 20, was top scorer in the Danish Superliga last season, netting 18 goals in 32 appearances in his first full campaign in the top flight.
He has played for Denmark six times, scoring one goal.
The transfer fee was not announced, although reports have put it at around 8 million pounds ($12.3 million).
The deal is still subject to Cornelius completing a medical, Cardiff said on their website (www.cardiffcityfc.co.uk).
($1 = 0.6520 British pounds)