Gichuhi, who stood as a candidate for Family First at the last election, was confirmed as the replacement for former senator Bob Day by the High Court on Wednesday.
She says she will take a conciliatory approach to her new role.
“While my values will never change, my approach to matters before the Senate will be to take the best possible advice from all corners before finalising a particular position,” she said.
“I look forward to consulting with the government, the opposition and the Senate crossbench as I move towards playing an active and effective role in parliament.”
The Kenyan-born lawyer arrived in Australia with her husband and children in 1999 and became an Australian citizen in 2001.
She is expected to be sworn into the Senate next month.
Earlier this month, the High Court ruled Day was ineligible to have been elected in 2016 because he had indirectly benefited from a government lease arrangement on his Adelaide electorate office.
Local News Matters
Media diversity is under threat in Australia – nowhere more so than in South Australia. The state needs more than one voice to guide it forward and you can help with a donation of any size to InDaily. Your contribution goes directly to helping our journalists uncover the facts. Please click below to donate to InDaily.