Environmental campaigners will sleep out in tents overnight to maintain their blockade.
The Extinction Rebellion protesters turned up at 10am on Monday morning and say they are planning to stay all day and all night throughout the week until Friday.
Protester Sara Han, says the group will try to occupy the bridge on Neville Street for the whole 5 days. They do not plan to move.
She is also a lecturer at the University of Leeds.
She said: "As a lecturer, I am preparing students for a future that just isn't going to be there for them.
"We are destroying the planet and what we're asking the government to do is to tell us the truth about a climate emergency. We want them to declare a climate emergency and we want them to act now."
Sara Han estimates that between 500-1000 protestors will come over the 5 days. She says people coming in for Manchester, Liverpool & across north to help hold the bridge.
She added: "The plan for the week is to hold the bridge and to have it as a point of focus, to shine a light on the role of finance in the fossil fuel industry which is contributing to the climate breakdown.
"We're going to have talks, workshops and speakers but it will remain peaceful - we wont be using any contentious forms of protest.
"A lot of people here will be camping overnight. There are people with tents and bags and people are planning on holding the bridge."
Dr James Chan, an A&E doctor across west Yorkshire, said: "The biggest threat to humanity is climate change. Our planet needs this action in order to survive.
"As a doctor, I know it is the single biggest threat to our health."
A spokesman for Extinction Rebellion said: "Activists from Extinction Rebellion are on Victoria Bridge in the centre ofLeeds.
"They have installed a bright yellow boat and are currently setting up a protest camp to shine a spotlight on the role of Leeds’ financial sector in financing polluting investments in fracking, coal and other dirty technologies.
"The protest is part of a ‘Summer Uprising’ across England, Scotland and Wales. Synchronised actions are currently taking place in Cardiff, London, Bristol andGlasgow.
"Each city will focus on a different aspect of the environmental crisis. The activists are aiming to remain on the bridge throughout the coming week, with many willing to risk arrest as part of a campaign of civil disobedience designed to press government and business to act now."