Boulter beat fellow Briton Heather Watson 6-4 7-5 before Burrage upset France’s Alize Cornet 7-5 7-5.
Both players will be appearing in their first WTA final with the British number one ranking also up for grabs.
“I was not expecting this coming into this week but I’m very, very happy with my performance,” 24-year-old Burrage said. “Alize is not an easy opponent to put away.
“It’s going to be an amazing day on Sunday and I’m really looking forward to it — what an amazing tournament for us.”
It is a stark contrast to the French Open where not one British woman made the main draw.
The last time two British women featured in a WTA Tour final was when Sue Barker played Virginia Wade in San Francisco in February 1977.