The 26-year-old Dutchman has penned a four-year deal with the Scottish champions and becomes the fourth new addition to the Celtic squad in the close-season.
Boerrigter helped Ajax to back-to-back Eredivisie titles during his two seasons in Amsterdam and had previous spells in his native Netherlands at RKC Waalwijk and Zwolle.
Celtic manager Neil Lennon must now decide whether or not to play Boerrigter in his side’s third qualifying round tie against Elfsborg.
Lennon has spoken openly about the Boerrigter transfer in the build-up to the game against the Swedish side.
"He is the type of player we have been looking for, for a while," said Lennon.
"He is a very fast, direct, left-footed player who has goals in him with his left and right foot.
"He is also very powerful. He has good experience and he has played at a high level for the last two or three years."
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