On Friday, the High Court of Australia ruled that five politicians were invalidly elected under the constitution because they held dual citizenship.
Mr Parry inherited British citizenship from his father.
The senior government figure said he was making the announcement with "a heavy heart" after receiving confirmation from the British Home Office.
Mr Parry's role as Senate president is to preside over Australia's upper house, mirroring the role of the speaker in the lower House of Representatives.
A replacement for Mr Parry will be chosen through a recount of votes from last year's election. It is likely to be another member of the Liberals, the senior party in the governing coalition.
He becomes the third government member to lose his job over the saga, following the disqualifications of Deputy Prime Minister Barnaby Joyce and Regional Development Minister Fiona Nash.
Mr Joyce and Ms Nash were members of the Nationals, the junior coalition partner.
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