The actress, who has also appeared in Emmerdale and EastEnders, was joined by Jane Thomas in a contest to secure the Labour nomination for the Batley and Spen by-election on October 20.
On Friday night, Ms Brabin won the selection to fight for the West Yorkshire seat has been vacant since Mrs Cox was shot and stabbed to death on June 16.
Labour Party members in the constituency chose their preferred candidate following a hustings event.
Other major parties, including the Conservatives, Liberal Democrats and Ukip, have said they will not field a candidate in the by-election out of respect for Mrs Cox’s memory.
But Labour does not expect the election to be “completely uncontested”, with Liberty GB and the English Democrats among those previously stating they will contest the seat.
If they do not, the selected Labour candidate would expect to automatically take the seat.
Ms Brabin was born in Batley and worked with Mrs Cox on her campaign to save the town’s library.
She played Tricia Armstrong in Coronation Street in the 1990s before appearing as Roxy Drake in EastEnders, and Carole in Emmerdale.
The news came as it was revealed that Ms Cox’s husband and children had flown to America at the invitation of President Barack Obama. President Obama will meet Brendan, Cuillin and Lejla Cox later. This was an invitation which the President made when he called Mr Cox shortly after Jo’s death to express his condolences.
Mr Cox said: “The kids are hugely excited and spent most of the flight doing drawings to give to the President. It’s a very thoughtful gesture and the kids are looking forward to telling him more about their mum.”
Meanwhile, EU chief Martin Schulz caused outrage after blaming Ms Cox’s death on the ‘nasty’ referendum campaign. In an extraordinary claim, the European Parliament president said her death was an example of how unpredictable the EU referendum campaign was. Former colleagues of Mrs Cox hit out at Mr Schulz over his comments, which were made during a lecture on Brexit at the London School of Economics.