The 26-year-old is currently undergoing a medical in Glasgow after the two clubs reached an agreement over the transfer fee.
Boerrigter, who has one year left on his deal at Amsterdam ArenA, is set to become the second Dutch player to arrive at Parkhead this summer, following the transfer of Virgil van Dijk from Groningen.
The talented footballer arrived at Amsterdam ArenA from RKC Waalwijk two years back and he proved to be an instant hit at the club.
Boerrigter went on to score 12 goals in 47 Eredivisie appearances, but eventually lost his place in the starting line-up to youngster Victor Fischer.
After Bojan Krkic arrived on loan this summer, the highly rated forward decided to leave in search of first team football and he is now set to embark on a new challenge.