It comes after the scheme was extended until October earlier this month.
Sunak confirmed that employees on the scheme would continue to be entitled to 80% salary payment up to a limit of £2,500 a month gross until October.
Until 30 June there will be no changes to the scheme.
From 1 August, employers will be asked to pay national insurance and employer pension contributions for employees on the scheme.
From 1 September, taxpayers will pay 70% and employers will be asked to contribute 10%.
From 1 October, this will change to 60% from the government and 20% from employers. The scheme will end at the end of October.
The chancellor also announced new “maximum flexibility” for employers who want to bring back employees part time.
From 1 July, employers will be able to bring back employees part time. If an employer brings back an employee two days a week, they will pay for this and the government will then pay for the remaining three days.
Sunak said: “As we enter this new phase things will change, businesses will need to become Covid secure.
“We need to adapt the emergency programmes we put in place.
“As we reopen the economy there is broad consensus the furlough scheme cannot continue indefinitely. I believe it is right in the final phase of this eight-month scheme to ask the employers to contribute alongside the taxpayer to the wages of their staff.”