Labour lost control of the borough for the first time in 16 years in a devastating set of local elections for the party on May 7.
While Labour remains the largest party in the town hall with 29 councillors, it lost 22 seats and fell short of holding a majority.
The Southwark Green Party's 22 councillors and the Liberal Democrats, who won 12 seats, now intend to form a joint administration at the annual meeting of the council tonight.
It means James McAsh, a former Labour councillor who defected to the Greens earlier this year, will become leader of the local authority.
He said: “Following our historic success at the local election, the Southwark Green Party is ready to form a Joint Administration. Southwark residents voted for hope - and this Joint Administration will deliver real change. We will make our borough more affordable and greener.
"Labour cuts have left the Council with an £85 million funding gap. We will stand up for our borough. This Council will now be accountable to Southwark residents, not to Keir Starmer. Together, our two parties can transform this council into one that genuinely listens, and where our diverse communities can shape decisions about where we live."
Victor Chamberlain, Southwark Liberal Democrat Group Leader, added: “Southwark Liberal Democrats have spent 16 years standing up for residents and holding Labour to account - and voters have now sent a clear message that Southwark needs change.
"I’m thrilled that we have been able to put party politics aside to put residents first through this proposed Joint Administration. Together, we will focus on fixing housing, making our streets cleaner and safer, and building a Council that listens and delivers for local people.”
Sir Keir Starmer’s experienced a disastrous set of local election results in the capital on May 7, losing control of 11 London councils and more than 350 seats.
The Greens meanwhile saw a meteoric rise and now have 297 seats in the city, a net gain of 248.
The party won control of councils in London for the first time in the party’s history, securing majorities at Hackney, Lewisham and Waltham Forest.