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Most international moving companies do not have their own offices world-wide; they work through a network of agents to arrange moves to/from practically anywhere. 

Intlmovers.com allows you to search for international moving companies which operate between your country of origin and Finland . If you wish, you can complete an online quotation request which will be submitted to the companies you choose from the resulting list. The site also provides information on planning, family guidance, law and more.
Website: www.intlmovers.com

Buried under boxes in your not-so-big Finnish apartment?   Omavarasto provides secure self-storage facilities, accessible by car or van, in Helsinki, Espoo and Oulu.
Website:  www.omavarasto.fi/en.html

The following companies are well established in Finland : they can arrange door-to-door international moves via land/sea/air freight, packing& unpacking, insurance, and customs clearance.

Victor EK: http://www.victorek.fi/	Finnish company established in 1885, specializing in moving, shipping and forwarding services.
Beweship:  http://www.beweship.com/	Independent Finnish moving, freight forwarding and transportation company.
Schenker: http://www.schenker.fi/	Schenker is part of the biggest land transport network in Europe as well as offering air and sea freight world-wide.('English' button at top-right)
Kalgin: http://www.kalgin.com.au/	Ex-Australia and Ex-New Zealand. Kalgin International Freight Services is a freight forwarding company with a worldwide network. From Australia : http://www.kalgin.com.au From New Zealand : http://www.kalgin.net.nz
Airport Travel Cargo: http://www.travelcargo.fi/	Finnish company providing freight forwarding, transport, household removals and courier services - also handles excess baggage.
Niemi: https://www.niemi.fi/	Niemi provides domestic household moving services and office relocation services. ('English' button at top-right)
DHL  Finland:    http://www.dhl.fi/	Courier services as well as land transport and air and ocean freight world-wide.