Independent South Australian senator Lucy Gichuhi has defected to the Liberal party in a surprise move giving the prime minister a much needed additional seat in the senate.

Malcolm Turnbull welcomed the new Liberal member to the party on Friday outside parliament.

“Those values – freedom, enterprise, getting ahead, opportunity - they are liberal values and you embody them ... welcome to the Liberal family,” Turnbull said in a video posted on Twitter.

Gichuhi took the seat of Family First senator Bob Day following a vote recount after he was ruled ineligible to stand for election.

She then quit Family First after it merged with the Australian Conservatives.

In the social media video the new Liberal senator said she thought the move would help her serve South Australians.

“I didn’t discover that until I did my maiden speech and I thought wow - I can’t believe how liberal I am at the core,” Gichuhi said.

The shock move has improved the Coalition government’s position in the senate, bringing the total of seats to 29 to Labor’s 25.

But the government will still need the support of the crossbench in order to pass legislation.

The defection is another boost for Turnbull after the resignation of Labor MP David Feeney who was unable to prove he was no longer a British citizen.

The Greens are a big chance to win the by-election in Feeney’s seat of Batman, which would give the government some breathing space in the lower house where it currently holds a one-seat majority.