Inkster led the home side to a five-point victory in Iowa last August after overseeing a record comeback from 10-6 down in Germany in 2015.
The 57-year-old will look to make it a hat-trick at Gleneagles in 2019, where home favourite Catriona Matthew will captain the European side in their own pursuit of a hat-trick of victories on Scottish soil following wins at Dalmahoy (1992) and Loch Lomond (2000).
"This is an unbelievable honour and one I do not take lightly," Inkster said. "I'm so stoked to be able to take the US team to Scotland, the home of golf, to compete in the 2019 Solheim Cup. We can't wait to get started."
Inkster is the first three-time captain for the United States. Europe were led by Mickey Walker in the first four contests (1990, 1992, 1994, 1996).
European captain Matthew made her ninth appearance as a player in Iowa, having originally served as an assistant captain to Annika Sorenstam.
The 48-year-old switched roles at the last minute after Suzann Pettersen withdrew through injury and won three points from four matches to take her career total to 22, third on the all-time list behind Laura Davies (25) and Sorenstam (24).
Matthew's personal heroics proved in vain as the visitors lost by five points to suffer a second straight defeat, but she is now focused on regaining the trophy on the same Centenary Course at Gleneagles where Europe won the 2014 Ryder Cup.
"Congratulations to Juli on this announcement. She's done an amazing job in the last two Solheim Cups, and throughout her Solheim career, and will certainly be a formidable opponent at Gleneagles," Matthew said.
"Juli is someone who I have admired very much over the years in all that she has achieved both on and off the golf course, and I am delighted she will be my opposite number for the 2019 match. I've definitely picked up some valuable insights into Juli's captaincy style over the last two matches, so I am excited we are both now in place and are ready to get down to business."
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