The Treasury said he will pledge the new funding in his spending review on Wednesday, when he will also deliver his long-term plan for infrastructure investment.
The majority of the spending is planned to go on specialist services for young people, including in schools, and support for NHS workers.
But Mr Sunak is also expected to make a vow for rapid progress to tackle the backlog of adult mental health referrals.
The Government estimates that mental ill health costs the economy up to £35 billion per year, and hopes the package will address the extra demand for services from the pandemic.
Mr Sunak said: “The pandemic has had a major impact on mental health because of increased isolation and uncertainty.
“So it is vital we do everything we can to support our mental health services and ensure help is there for people.
“This funding will make sure those who need help get the right support as quickly as possible so they don’t have to suffer in silence.”
Mr Sunak’s spending review is long-awaited, but it could also spark industrial action if he confirms the Government will impose a pay cap on millions of public sector workers.
Unions reacted angrily to reports the Chancellor would announce a pay limit at the spending review, though frontline NHS doctors and nurses are expected to be exempt.
Labour shadow chancellor Anneliese Dodds urged Mr Sunak on Saturday to use his spending to prevent a return to the conditions that allowed the UK to be “so badly hit by the pandemic”.
She said the Chancellor “must lay the foundations for that recovery” in his set-piece financial update on Wednesday to prevent protective equipment stocks dwindling, local services returning to being “on their knees”, and families being left with little savings and “struggling with the cost of living”.
“And that must include working together to build a better, more secure future for our country, so that we do not go back the fragility and instability of the way things were,” she told the Co-operative Party’s local government conference.
Mr Sunak will also unveil the much-delayed National Infrastructure Strategy for £100 billion of long-term spending to help tackle the climate crisis and invest in transport.
It was also confirmed Mr Sunak will change the Treasury’s “green book”, a set of rules to determine the value of Government schemes which is thought to favour London and the South East of England.