She said she was “overwhelmed and humbled” by the support she had received from party members in the seat her sister used to represent.
Her selection was welcomed by party leader Sir Keir Starmer who said her roots in the community would make her a “fantastic champion” for the constituency.
“Batley and Spen holds an important place in the Labour Party’s heart. And Kim’s work to bring people together, just as her sister Jo Cox did, has inspired us all,” he said.
It comes amid amid warnings it could be “curtains” for Sir Keir if the party loses.
Ms Leadbeater will be up against the Leeds councillor Ryan Stephenson, chairman of the West Yorkshire Tories.
The contest was triggered by the decision of Labour MP Tracey Brabin to quit Westminster following her election as the first mayor of West Yorkshire.
It was previously represented by Mrs Cox until she was shot and stabbed by a far-right extremist in June 2016.
Ms Brabin tweeted: “Congratulations to friend and campaigner @KimLeadbeater7 who smashed it! She’ll do #batleyandspen proud!
“It’s going to be tough but I know we can win for #BatleyAndSpen.”
Labour is desperate to hold on to the seat following the party’s crushing defeat in another “red wall” by-election in Hartlepool earlier this month.
The result triggered a bitter round of recriminations, with the Labour left – marginalised under Sir Keir – gunning for the party leader.
Former shadow home secretary Diane Abbott – a close ally of ex-leader Jeremy Corbyn – said it could be “curtains” for Sir Keir if they lose again.