After reaching adulthood and graduating from Yale in 1874, Brady became a Presbyterian minister and was one of that denomination's first pastors in Alaska (1878), where he also established a school for Native Alaskan children. He left the ministry and became active in the logging industry. He was appointed territorial governor in 1897 and continued to press for Native Alaskan civil rights, but he resigned in 1906 after a critical enquiry into his involvement with the Reynolds-Alaska Development Company fraud (he was later exonerated). He had diabetes.