The Argyle Street development will include 160 rooms and 68 serviced apartments. It will be aimed at the luxury market.
Glasgow City Council planning officials described the project as a "landmark development" that would act as a gateway to the redeveloped Broomielaw district.
Progress Property chief executive officer Charles Price said he is delighted to be involved in helping Glasgow to achieve its tourist ambitions.
Green councillor Nina Baker argued unsuccessfully that the building should be restricted to 11 storeys to avoid it casting shadows over neighbouring homes.