Vandeweghe was drawn to face Aliaksandra Sasnovich in the first singles match. U.S. Open champion Sloane Stephens will then play Aryna Sabalenka.
Kathy Rinaldi, in her first season as the U.S. captain, is trying to become the first since Billie Jean King to lead a winning Fed Cup squad.
"We know we're going to have a very competitive weekend," Rinaldi said. "We're going to have each other's backs and compete as a really tight-knit team."
Stephens retired from a match with a knee injury in China last week. She says she's ready to play on the indoor hard court.
"Really looking forward to getting back on the court," the 13th-ranked Stephens said. "I'm excited to be here for a final. Just hoping to have a great weekend."
The Americans won a record 17th Fed Cup title in 2000, with King as captain. Since then, they have played and lost in three finals - 2003, 2009 and 2010. Belarus is playing in the Fed Cup final for the first time.
"You just try your best," Vandeweghe said Friday. "Doesn't matter if I play first, second, not at all. I'm out here for these girls, to compete as hard as I can."
On Sunday, Vandeweghe will go up against Sabalenka, and Stephens will meet Sasnovich. In doubles, the final match of the best-of-five series, Alison Riske and Shelby Rogers will play for the United States against Vera Lapko and Lidzlya Marozova.
The draw ceremony was presented with a nod to traditional Belarusian culture. There was an archer who perfectly placed an arrow through a tennis ball, which contained Sasnovich's name, to determine the order of play.
The official photos featured all the competitors holding swords. Two men dressed in knight's attire on horseback greeted draw attendees outside the Minsk City Hall.
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