The 23-year-old Finland international puts pen to paper on a four-year contract, becoming Neil Lennon's sixth signing this summer for the reigning Scottish champions
The 23-year-old forward, who scored three goals in 17 Bundesliga appearances last season, has signed a four-year deal with the Scottish champions.
The Finland international is Celtic's second completed transfer within the space of 24 hours following the arrival of Israel midfielder Nir Biton from Ashdod on Friday.
Despite featuring in the Champions League play-offs for Schalke, Pukki is eligible to play for Celtic in the group stages.
Pukki started his career at FC KooTeePee before moving to Sevilla in 2008. The forward returned to Finland in 2010 with HJK Helsinki and was signed by Schalke just over a year later.