The 26-year-old becomes Neil Lennon's fourth signing of the summer and could make his debut in the UEFA Champions League against Elfsborg on Wednesday if international clearance comes through in time.
Boerrigter played for FC Twente at youth levels before joining Ajax in 2006, but he left after a season on loan with Haarlem and returned in 2011 after spells with FC Zwolle and RKC Waalwijk.
He played 47 times for Ajax in his second stint, scoring 12 goals, and he did enough to earn his first call to the Netherlands side, but he was unable to take it up because of a back injury.
Boerrigter joins fellow Dutchman Virgil Van Dijk, Amido Balde and Steven Mouyokolo as new faces in the Celtic squad ahead of their title defence.
Lennon said: "He is the type of player we have been looking for, for a while. 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."