Ground-breaking at the plant in Aabenraa, which will employ between 50 and 100 people, will start in the final quarter of 2017, with construction due to be completed in early 2019.
The facility will help to handle data from iMessages, answers from the voice-activated assistant Siri and song downloads from iTunes, Apple's director for the Nordic countries, Erik Stannow, said.
Supercomputers at data centres generate large amounts of heat, which requires high levels of electricity for cooling.
Easy access to 100-percent renewable energy and the reliability of the Danish grid motivated the decision, Apple said.
The US electronics and online services giant invested a similar amount in a data centre in Viborg, northern Denmark, in 2015.
The firm has contracted with an energy supplier to provide more than 30 megawatts of wind-generated electricity.
Correction: an earlier version of the article incorrectly stated the value of the investment in Danish kroner as nine billion.