Molik is stepping down after leading the team for a decade, guiding them to the finals in 2019 and 2022, which was Stosur's tournament swansong.
"I've got years of playing experience and one thing that I know is how the girls feel when you walk out on the court to play for Australia," the 39-year-old Stosur said.
Stosur contested 34 Billie Jean King Cup ties after making her debut in 2003 and holds the record for most singles wins –- 29 –- by an Australian player in the competition.
She won the 2011 US Open and reached a career-high of world number four that year.
Stosur is also a four-time Grand Slam doubles and three-time mixed doubles champion.
