Speaking at the scene near Nelspruit, police spokesman Captain Leonard Hlathi said the bus was carrying a group of students, who were due to return home to the UK tomorrow.
He said: "There was a bus crash and two of the passengers, both female, passed away at the scene.
"Twenty of them were taken to the hospital and one of them was described as critical and was airlifted to Nelspruit Medi Clinic.
"It happened about an hour ago. The driver apparently lost control and overturned.
"The two bodies are being removed from the wreckage."
He said the 20 injured included 18 Britons, the tour guide and driver.
The passengers were believed to be college students aged about 19, who had arrived in the country on June 1 and were due to return to the UK tomorrow.
The accident happened a few miles from Barberton on the Bulembu road.
A British High Commission spokesman said: "We are aware of reports of a bus crash in Nelspruit.
"We are working very closely with the South Africa authorities to try to ascertain more details."
South Africa's roads are notoriously dangerous.