Griest was one of two women who made history last year after becoming one of the first female soldiers to pass the army's grueling course to qualify for the elite Rangers unit.
Three women on course to make US Army Rangers history
Earlier this month, the army said it had approved requests from more than 20 women to enter the infantry and armor branches, both of which face the possibility of combat. The armor branch includes tanks.
Army Times, which first reported the news, said Griest was expected to graduate from the Maneuver Captain's Career Course on Thursday.
Last year the US military said it would let women serve in all combat roles, a historic move striking down gender barriers in the armed forces.
US military to open frontline combat roles to women
As of mid-2015, nearly 12 per cent of US forces deployed to Iraq and Afghanistan were women. They represented about 2 per cent of US military deaths in those wars.
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