The pandas are to be loaned from China to Denmark as a mark of the good relationship between the two countries.
“We are warmed by the thought that we are today beginning the groundwork for a new panda paradise.
“This is only possible because so many people have worked so hard for such a long time,” Rasmussen said prior to work beginning on Thursday.
High-profile architect Bjarke Ingels designed the enclosure, which will cost up to 150 million kroner (20 million euros) and will be formed in the shaped of the yin and yang symbol.
The building will be placed at the site of Copenhagen Zoo's former elephant house.
Ingels said that he was surprised at how well pandas are suited to Denmark's climate.
“Where the pandas come from in China has more or less the same climate as [Copenhagen neighbourhood] Frederiksberg,” Ingels said.
A number of foundations and institutions have supported the project to bring the two pandas, Mao Sun and He Xing, from Chengdu Panda Base in China to the Copenhagen zoo.
The loan agreement is valid for ten years with the option of extension.
“I hope we can keep the pandas for the duration of their lives,” Rasmussen said.