The forward is the second player to arrive in the East End of Glasgow this week, joining Israeli midfielder Nir Biton, who signed on Friday.
Despite playing in Champions League qualifiers for Schalke, Pukki is eligible to play for Celtic in the group stages of this year's competition.
Pukki told the Celtic club website: "This is a big opportunity for me and I'm really happy to be here.
"Of course, I was thinking that this would be a good place for me. I want to win the championship & it'll be great to play in the Champions League."
Pukki moved to Germany from HJK Helsinki in a £1.3m switch but made just seven starts over two seasons as he was restricted largely to substitute appearances.
He started his career with FC KooTeePee and also had spells in Spain with Sevilla and Sevilla Atletico.
On the international stage, he has scored six times in 25 appearances and scored the equaliser in a 1-1 draw with Spain in a World Cup qualifier in March.