Capped for the first time this year, Yamada said a public goodbye to Kawasaki fans after Wednesday’s Emperor’s Cup defeat at home to SC Sagamihara.
He leaves his former club sitting sixth in the J-League after 23 matches, having scored twice in his 21 outings.
Yamada follows fellow forwards Benjamin Nygren and Callum Osmand, defenders Hayato Inamura and Kieran Tierney and goalkeeper Ross Doohan in joining the Scottish champions this summer.
“Celtic is one of the top names in world football,” said Yamada. “I have already watched my countrymen Daizen [Maeda], Reo [Hatate] and Kyogo [Furuhashi] do so well at Celtic and I will aim to have the same impact.
“I am my own player, though, and I am ready to face all my own challenges directly.”