Malaysia on Saturday appointed a former judge as its new anti-corruption chief in an unprecedented move, as the government seeks to calm months of political turbulence over alleged misconduct linked to the watchdog’s outgoing head.

Allies and opponents have hit out against Prime Minister Anwar Ibrahim since February following reports claiming that Malaysian Anti-Corruption Commission (MACC) boss Azam Baki was involved in a share ownership scandal and the agency’s officers were allegedly working...