The Chancellor will on Wednesday detail the plan to spend the new cash to aid the programme, which is a key factor in successfully easing lockdown restrictions.
Mr Sunak will also divert £22 million to fund a “world first” trial to test if different vaccines can be used together, or if a third dose is effective, the Treasury said.
NHS England has begun inviting 60 to 63-year-olds to book jabs, with nearly 20 million people across the UK having received a vaccine.
Ahead of his Commons speech, Mr Sunak said it is “essential we maintain this momentum”.
“Protecting ourselves against the virus means we will be able to lift restrictions, reopen our economy and focus our attention on creating jobs and stimulating growth,” he added.
He will also give £33 million to improve the ability to respond to new variants and improve vaccine testing, including £5 million to create a “library” of Covid-19 jabs.
That cash, like the funding for the vaccine trial, will come from the Vaccine Taskforce’s existing budget.
The government is reviewing whether vaccine passports could be used to prove people’s health status before entering venues such as pubs and theatres.
Mr Sunak said the conclusions should come in a “few months’ time”, as he acknowledged both their potential benefits as well as their challenges.
“Obviously it’s a complicated but potentially very relevant question for helping us reopen, particularly those parts of our country like mass events,” he told The Andrew Marr Show on the BBC.