Murphy served as interim manager for the Padres in 2015, leading the team to a 42-54 record over the final 96 games of the season. He became bench coach of the Brewers in 2015.
Murphy stepped in as manager for one game in 2023, when Counsell was absent. The Brewers lost 8-6 to the Oakland Athletics.
Counsell, who led the Brewers to a 707-625 record over nine seasons, left the team earlier this month to become manager of the Chicago Cubs.
The longtime Brewers infielder won two World Series titles, with the Florida Marlins and Arizona Diamondbacks, during his 16-year MLB playing tenure. As a manager, he led the Brewers to three National League Central division titles and three seasons with at least 90 wins.
The Brewers went 92-70 to win the division title again in 2023. They then lost to the Diamondbacks in a National League Wild Card Series.