In the original Williamsburgh Street grid, Driggs Avenue was Fifth Street, running from Division Avenue to the Williamsburgh/Greenpoint line. By 1879, Fifth Street extended as far north as Leonard Street in Greenpoint. North of Leonard Street the street continued to Meeker Avenue as Van Cott Street.
In 1886 Fifth Street was renamed Driggs Street (not Avenue), and the numbering was turned around to start at the north. The north then was North 13th Street, in the midst of what was still then Bushwick Creek. Van Cott Street, during this period, was extended from Leonard Street south to Banker Street (which intersected with Driggs at North 13th).
Sometime between 1889 and 1897 Driggs Street was renamed Driggs Avenue and extended to encompass all of what was previously Van Cott Street. At this point, the street numbering was changed yet again, to start at Meeker/Morgan and continue south to Division Avenue.