Mr Sunak used his Budget speech to reveal that the new site in Yorkshire's biggest city "will invest across the UK in public and private projects to finance the green Industrial Revolution, beginning this spring".
The bank will channel billions of pounds into capital projects as part of the UK government’s “levelling-up agenda”, according to government officials.
The Treasury believes that the new institution can play a key role in helping to kickstart Britain’s economic recovery in the wake of the pandemic.
The new lender will have a remit to help deliver the UK’s commitment to reach “net zero carbon” by 2050 and provide funding for projects across the UK.
It will co-invest alongside private investors through a mix of loans and guarantees as well as taking equity stakes in projects.
The new infrastructure bank was recommended by John Armitt, the head of the National Infrastructure Commission — an arms-length government body — who said it should start with an asset base of £20bn.
The new bank is in part designed to replace funding previously obtained from the European Investment Bank, which the UK is leaving after the Brexit transition period which ends on December 31. The EIB previously lent about €8bn a year for projects ranging from London’s Crossrail line to social housing and new school-building projects.
Mr Sunak told the Commons today: "If we want a better future economy, we have to make it happen. We have to do things that have never been done before.
"The world is not going to be any less competitive after coronavirus. So it's not enough to have some genuine desire to grow the economy. We need a real commitment to green growth.
"It's not enough to have some general desire to increase productivity, we need a real commitment to give every business large or small, the opportunity to grow, innovate and succeed.
"It's not enough to have a general desire to create jobs. We need a real commitment to create jobs where people are and change the economic geography of this country.
"And we can't strengthen our domestic economy without remaining a global outward looking nation. This future economy won't be created in any one budget. But today we lay the foundations.
"Our future economy needs investment in green industries across the United Kingdom, so I can announce today the first ever UK infrastructure bank. Located in Leeds the bank will invest across the UK in public and private projects to finance the green Industrial Revolution, beginning this spring.
"It will have an initial capitalization of 12 billion pounds, and we expect it to support at least 40 billion pounds of total investment in infrastructure. And I know my Right Honourable friend the member for Pudse (Stuart Andrew) will particularly welcome the location of this new institution."