Plitzuweit replaces Mike Carey, who retired two weeks ago after 21 seasons.
"Dawn is a proven winner everywhere she has been, and her track record for sustained success is impressive," West Virginia athletic director Shane Lyons said in a statement. "When we started our search, it was quite obvious that her reputation as a program builder and championship coach put her at the top of our list."
Lyons said Plitzuweit will have a five-year, $3 million contract with a starting salary of $550,000, plus incentives.
Plitzuweit went 158-36 in six seasons at South Dakota, including four NCAA tournament appearances. She was named the Summit League Coach of the Year three times.
She won a Division II national championship in 2006 as the coach at Grand Valley State in Michigan. Plitzuweit is from West Bend, Wisconsin, and played at Division II Michigan Tech.
Plitzuweit has the task of replacing West Virginia's all-time winningest coach. Carey went 447-239 but had just one NCAA tournament appearance in the past five seasons and never took the Mountaineers past the second round in his career.
"I just cannot wait to get to Morgantown to meet with our team and to connect with them," Plitzuweit said.
She will inherit a team that went 15-15 this season and lost leading scorer KK Deans to the transfer portal last week.