[Lucy Gichuhi in a past event. She has become the first Kenyan to win senatorial seat in Australia. Photo/the-star]

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Kenyan - born lawyer Lucy Gichuhi has won the South Australian Senate seat after the High Court ordered a recounty on the votes.

She is set to replace former senator Bob Day in the Senate.

Speaking to ABC News on Wednesday, Gichuhi welcomed the high court's decision, vowing to serve diligently in her new position.

"I am honoured and grateful for this opportunity to serve Australia. I see it as an opportunity to give back to this great nation," she said.

"I do not intend on commenting on the processes that have brought us to this point. As a lawyer, I am deeply respectful of both the legal and electoral processes. I am an Australian citizen and am eligible to serve. I will continue to take advice on all of these matters as we move forward," she added.

Ms Gichuhi moved to Australia in 1999, before acquiring full citizenship in 2001.

She is set to become the first person of African descent to sit in Australia's 76-seat Federal Parliament.