Youth Olympic silver medallist Mica McNeill and team mate Mica Moore had appealed for 30,000 pounds in September after being told there was only enough money for the men.
The pair, who won the world junior title last year, exceeded that amount within six days.
British bobsleigh's governing body freed up more funds after the departure later that month of chief executive Richard Parker.
"It’s a dream come true to compete at an Olympic Games," said McNeill, who was fourth with Moore in the European Championships in Igls, Austria, in December and will be competing at her first Games.
"Four months ago my career was uncertain and to be selected today is very emotional but incredible and I’m so excited."
Women's bobsleigh was added to the Olympic programme at the 2002 Salt Lake City Games and Britain has yet to win a medal in it.
The men have won four medals over the years, including two-man gold in 1964 and a four-man bronze in 1998.
They could also collect a retrospective bronze from the 2014 Sochi Games since two Russian sleds ahead of them have been disqualified for doping offences.
(Reporting by Alan Baldwin, editing by Ed Osmond)
