The government wants to "renew the UK's position as the world's pre-eminent financial centre" following Brexit, the chancellor said.
Making a statement in the Commons, Mr Sunak said financial services "will be essential to our economic recovery from coronavirus, creating jobs and growth right across our country".
Germany, France and the Netherlands have issued their own green bonds and European Commission President Ursula von der Leyen said in September that 30 per cent of the EU's coronavirus recovery programme should be funded in this way.
Investment in energy low-carbon energy infrastructure, reducing emissions from transport and retrofitting homes to make them more environmentally friendly are among measures being targeted by governments to help stimulate their economies in the wake of devastation wrought by the pandemic.
Through green bonds, governments can borrow money for these projects at low interest rates while giving steady, long-term income to investors such as pension funds which are seeking stable investments that benefit the environment.
Under plans unveiled on Monday, UK-listed companies will also be required to disclose the risks they face from climate change by 2025.
Mr Sunak said: "As we leave the EU and start a new chapter in the history of financial services in this country, we want to renew the UK's position as the world's preeminent financial centre."
He said he was setting out plans "to make this country more open, more technologically advanced and a world leader in the use of green finance".
The government has faced criticism from campaigners for not tying its support packages to environmental commitments.
However, Bank of England Governor Andrew Bailey said on Monday he believed ministers had taken the right approach.
"In the face of such an emergency in all conscience it was not right to say to people that they would be denied a livelihood because their employment was of the wrong sort for the climate," he said.
He added: "What we cannot measure we cannot manage, so it is important that financial firms and their clients use the [Taskforce on Climate-related Financial Disclosures] framework and the latest tools available to measure, model and disclose the climate risks and opportunities they are exposed to today and in different future climate scenarios.
"We at the Bank started to do this ourselves when we published our own climate disclosure this summer.
"We are now working with the Treasury and other regulators to consider the UK's approach to climate disclosure."
The global movement to face up to the climate crisis was boosted over the weekend with Joe Biden’s victory in the US presidential election election.
Mr Biden has pledged strong action on climate change, after his predecessor Donald Trump removed the country from the Paris Climate Agreement.