Pekka Nuutinen, Finland's incoming top immigration official, told public broadcaster Yle that the capacity of the centres would fall from this year's peak of 30,000 to 10,000 by the end of 2017.
Funding was a key factor behind the decision together with security and the location of the centres, Nuutinen said.
Some 32,500 people sought asylum in Finland in 2015 and the figure is expected to be just 10,000 this year and in 2017.
Like other Nordic countries, Finland, led by a centre-right government, has recently tried to discourage asylum seekers by tightening rules and reducing social benefits.