"Since my first appearance in 1998, I have always loved playing in the Solheim Cup," the 48-year-old three-times winner said in a statement.
"Scotland will provide the perfect stage for the 2019 Solheim Cup and Gleneagles will be a terrific venue...there is nothing better than winning in your home country."
The biennial tournament is contested by teams representing Europe and the United States.
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Matthew takes over as captain from Sweden's Annika Sorenstam, having previously served as a vice-captain.
The Scot has a career total of 22 Solheim Cup points, making her third on the all-time list after Laura Davies (25) and Sorenstam (24).
"She helped us a lot over the past year as a vice-captain, but then stepped in and won us three points as a player. Catriona is very well respected by the players, so she is a natural choice," said Sorenstam.
(Reporting by Alan Baldwin, editing by Toby Davis)
