The government also announced immediate plans to get care workers to do more health checks, and a funding boost for services to help elderly and disabled people remain in their homes.
Social care means help for older or disabled people with day-to-day tasks like washing, dressing, medication and eating.
Only those with the most complex health needs get social care provided free by the NHS, so most care is paid for by councils.
In England, only people with high needs and savings or assets of less than £23,250 are eligible for that help, leaving a growing number of people to fund themselves.
Some face paying hundreds of thousands of pounds for their care and may be forced to sell their own home as a result.
The government’s ultimate aim is “a new National Care Service, able to meet the needs of older and disabled people into the 21st Century”, said Streeting.
He said he had invited opposition parties to take part in the commission “to build a cross-party consensus to ensure the National Care Service survives governments of different shades, just as our NHS has for the past 76 years”.
Baroness Casey – who has led several high-profile reviews, including into homelessness, the Rotherham child exploitation scandal and the Metropolitan Police – said she was pleased “to lead this vital work”.
She is viewed in government as being straight-talking, with good cross-party links, and as someone who gets things done.
Even so, drawing up a plan for a National Care Service that meets the needs of an ageing population and is affordable is perhaps her biggest challenge yet.
There is agreement that the care system has been in crisis for years, struggling with growing demand, under-funding and staff shortages.
The problem has been getting political agreement on how overdue reform will be funded.
In 2010, Labour plans to fund social care were labelled a “death tax”‘ in that year’s election, and Conservative plans were called a “dementia tax” in the 2017 election.
There have also been numerous commissions, reviews and inquiries over the past 25 years which have failed to bring change.
The 2011 Dilnot Commission plan for a cap on individual care costs came closest, making it into legislation, but was not implemented.
It was finally scrapped by the new Labour government last summer because it said the last Conservative administration had not set aside the money to fund the reform.
However, providing enough support for people in their own homes, care homes and supported living remains a pressing issue.
The care systems in Scotland, Wales and Northern Ireland are slightly more generous, but all are facing the pressures of growing demand and squeezed finances.
