The band split with previous management , Mucho Bravado, late last year.
The deal is believed to be a co-manage arrangement, with Cullen focusing on Australia and Bryan looking at international opportunities.
The band are familiar with the Stop Start as they are signed a label deal with the company last year. They are also booked by Select, whose head Stephen Wade is a co-founder of Stop Start.
Their album Museum was released last October, was triple j's Album Of The Week and debuted at nine on the ARIA Album Chart.
Veterans lead this week's releases with new albums from Tim Rogers & The Bamboos (Album Of The Week) and Daniel Johns plus albums from Ella Thompson, The Vaccines and Unknown Mortal Orchestra.