When Kunnari become seventeen years old he moved to Tampere and started to study in Varala sport highschool.

He played in Vammala season 2000–2001 and 2001–2002 then he changed to a bigger team named Pielaveden Sampo.

After four seasons in Finland, Olli started his professional volleyball career in France, Pro A-league.

After France Pro A -league Kunnari made contract with Polish league team Olsztyn.

In the European Championships 2007 Finland's national team came in 4. place and Olli played arguably the best volleyball of his career.