The Coronation Street, EastEnders and Emmerdale star was chosen as the party's candidate ahead of fellow nominee Jane Thomas.
Mrs Cox, who was MP for Batley and Spen, was shot and stabbed in Birstall, West Yorkshire, on 16 June.
The by-election will take place on 20 October.
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, and has also written for shows including Family Affairs, Tracy Beaker and Hollyoaks.
Ms Brabin, who was selected at a hustings event on Friday, said she was "humbled and privileged" to have the chance to succeed Mrs Cox.
"Jo was my inspiration. I intend to do her proud," she said.
"Obviously no-one wanted this, but I'm the only person on the ballot paper that can stand up for everyone in Batley and Spen.
"I'm hoping people will put party politics to one side and we can work together."
Meanwhile, the husband of Mrs Cox has had a meeting with US President Barack Obama at the White House in Washington DC.
Brendan Cox, who took his two children, wrote on Twitter that he and the president had "talked about Jo" and "fighting extremism".
He praised President Obama as being "excellent with the kids", adding that "the kids gave him their best drawings".
Following the announcement of the selection of Ms Brabin, Yorks&Humber Labour â€
Former soap-actress Tracy Brabin has been selected as Labour's candidate for the Batley and Spen by-election prompted by the killing of Jo Cox.