The others announced at Gleneagles on Monday ahead of the Sept 11-13 tournament were England’s Bronte Law and Jodi Ewart Shadoff and France’s Celine Boutier.
The eight automatic qualifiers in the 12-strong team were confirmed on Sunday after the Scottish Open.
Sweden’s Anna Nordqvist took the last rankings spot to join compatriot Caroline Hedwall, Spain’s Carlota Ciganda — the highest ranked European in the world at 13th — and Anne van Dam of the Netherlands.
England’s Charley Hull and Georgia Hall, Spain’s Azahara Munoz and Germany’s Caroline Masson qualified via the world rankings.
Europe are looking to win the biennial trophy for the first time since 2013.
“Suzann’s come in as a pick, so she’s going to step down from her vice-captain role,” said Matthew of the Norwegian who has played only two events since her return this year, but is one of the most decorated players in Solheim history.
Pettersen, 38, said she would much rather play than be part of the captaincy.
“I’m really excited. I think this is a good winning team. The experience is good, a lot of great young players. Just really happy to be part of the team as a player.
“It’s been a little difficult, the last two years,” added the player who is ranked 620th in the world. “My life has changed a lot, obviously for the better, but I’ve missed golf over the last half a year and I’m very happy to be back in competition.
“It’s a massive honor for me to be here.”
Reporting by Alan Baldwin; Editing by Toby Chopra