Chancellor of the Exchequer Philip Hammond issued the guarantee following criticism that rural projects and proposals face an uncertain future following the Brexit vote.
Mr Hammond said: "The UK will continue to have all of the rights, obligations and benefits that membership brings, including receiving European funding, up until the point we leave the EU.
"We recognise that many organisations across the UK which are in receipt of EU funding, or expect to start receiving funding, want reassurance about the flow of funding they will receive."
There has been criticism that the guarantee does not go far enough – and lacks clarity.
But Mr Hammond said he was confirming that EU structural and investment funds projects signed before the Autumn Statement would be guaranteed by the Treasury.
"The government will also match the current level of agricultural funding until 2020, providing certainty to our agricultural community, which play a vital role in our country," he added.
Mr Hammond said the government was determined to ensure that people had stability and certainty in the period leading up to the UK's departure from the EU.
Defra secretary Andrea Leadsom described the guarantee of funding as "excellent news" for farmers and for the environment.
"I'm delighted we can provide this crucial certainty and continuity to our rural communities while we develop a new approach to supporting agriculture and protecting our precious countryside."
Local government secretary Sajid Javid said guaranteeing EU funding would further support the work of Local Enterprise Partnerships to rebalance the economy.
It would enable LEPs to plan ahead with certainty so businesses, universities and local authorities across the country could enable economic growth.
"This will be crucial as we work together to take advantage of the opportunities presented by the UK's decision to leave the European Union," said Mr Javid.