Chloe Allen, who joined the army four years ago as Ben, told the tabloid it was "a great honour to make history".
The defence ministry in July announced a lifting of the ban on women serving in combat roles.
The decision, which is being gradually implemented over three years, comes after the United States dropped its official ban on women in combat in January.
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Allen, 24, said she would "love to inspire people to just come out and be themselves".
She told The Sun: "As much as it's a big bad world, it's not as bad as people think and it's easier when you've got your mates and your bosses behind you."
General James Everard said: "I applaud Guardsman Chloe Allen for being a trendsetter and wish her every success."
He added that "the British Army is really proving itself as an inclusive organisation where everyone is welcome and can thrive".
Women currently account for about 10 percent of British military personnel.
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