The 36-year-old started limited catching of bullpen sessions Wednesday and took batting practice. Molina will appear in games at first as a designated hitter, and manager Mike Shildt is hoping he can catch against the New York Mets in two weeks.
"More than anything else, it was my first and only offer," said the 32-year-old Wieters, whose deal was announced Wednesday.
A four-time All-Star with the Baltimore Orioles from 2009 to 2016, Wieters spent the past two seasons with the Washington Nationals. He hit .238 with eight homers and 30 RBIs last year, when he was sidelined between March 31 and April 12 with a strained left oblique muscle and between May 10 and July 9 with a strained left hamstring.
"It will be exciting because this will be the first time I've competed for a spot on a roster since 2009," Wieters said. "I'm excited to kind of see what kind of adrenaline I get in spring training, which I haven't had in a while."
Shildt expects Wieters to make his St. Louis debut behind the plate early next week.
Molina averaged 133 games behind the plate over the past three seasons.
"I've watched him for as long as I can remember," Wieters said. "There aren't many catchers in this league I watched before I was playing in this league."