Minson was at one point the company's deputy CFO. He also has been CFO and chief operating officer at AOL.
Kini had been interim CFO and executive vice president of strategy and business insights since February.
Martin is senior vice president of corporate finance and investor relations. CFO John Bode is set to step down.
Hsia joined the company in 2011 as senior manager of internal audit, then was appointed deputy CFO.
Nallen is News Corp.'s deputy CFO. News Corp. CFO David DeVoe will retire when the company is divided to split off 21st Century Fox.
Cooper was CFO of Westell Technologies. He is taking over at Federal Signal from the interim CFO.