Seen as a continuity candidate, the shadow business secretary must overcome scepticism inside the party rooted in its crushing defeat by the Tories in the recent general election, which many blamed on Mr Corbyn.
Launching her campaign in the democratic socialist magazine Tribune, Ms Long Bailey said that “with the climate crisis spiralling and the far right on the march, we must regroup for the struggles ahead”.
She added: “Many candidates in the leadership election say they will not return to the triangulation and Tory-lite policies that held our party back before Jeremy.
“But we need a leader that can be trusted with our socialist agenda. A leader who is totally committed to the policies and has the political backbone to defend them.
“We need a proud socialist to lead the Labour Party, driven by their principles and an unwavering determination to see democratic socialism in our lifetime.
“For all of these reasons and more, I have decided to stand for election to become the next leader of our party. I don’t just agree with the policies, I’ve spent the last four years writing them.”
Ms Long Bailey joins five others – shadow Brexit secretary Sir Keir Starmer, shadow foreign secretary Emily Thornberry, Clive Lewis, Lisa Nandy and Jess Phillips – in the race to become leader of the opposition.
Ian Lavery, another Corbynite leftist, said after Ms Long Bailey’s announcement that he would not stand, choosing to support her instead.
The party’s ruling National Executive Committee announced on Monday that the new leader would be named on 4 April, with Mr Corbyn remaining in post for almost four months after taking the party to its worst general election defeat since 1935.
The postal ballot for the new leader and deputy leader will open on 21 February, before coming to an end on 2 April.