The health secretary said all 30,000 care providers would be contacted by the end of the week and offered tests for their staff.
Tests for care home residents showing symptoms of the disease would be prioritised as capacity increases, he added.
All patients discharged from hospital will be tested before they go to a care home.
Figures released yesterday show a tenth of coronavirus deaths could be happening outside hospitals, half of these inside care homes.
The figures, from the Office for National Statistics (ONS), cover the end of last month and the beginning of April, meaning the true numbers could be even higher now.
In recent weeks two of the UKs largest care home providers have also reported more than 500 deaths between them.
Mr Hancock has pledged the UK will be carrying out 100,000 tests by the end of this month but official figures released yesterday show just 14,000 tests were carried out on Sunday, down from 18,000 during the previous week.
At the moment the first five residents in a care home to show symptoms of Covid-19 are tested, to confirm whether or not there is an outbreak.
But the government is to change the rules, so that anyone with symptoms can have a test,
Ministers are expected to set out more detail on their Covid-19 social care action plan later today.
Mr Hancock said he was “deeply conscious that people in residential care are among the most vulnerable to coronavirus”.
“We are doing everything we can to keep workers, residents and their families safe, and I am determined to ensure that everyone who needs a coronavirus test should be able to have access to one,” he said.
“We have already begun testing social care workers and will roll this out nationwide over the coming days. And as we continue to ramp up our testing programme, we will test all current care home residents with coronavirus symptoms and all new care home residents who are discharged from hospital into care.”
As part of the plan ministers would ensure all care home residents who need a test “can have a test,” he added.
Labour’s social care spokesperson Liz Kendall said: “Increased testing for care home residents and care staff is essential to tackling the emerging crisis in social care and something Labour has long been calling for. We look forward to seeing details of how this latest commitment will be delivered, with only 500 care staff having been tested to date.
“The Government has rightly said the NHS will get whatever resources it needs to deal with the Covid-19 pandemic. This must also apply to social care, which needs a much greater priority and focus than it has had so far.”
“Alongside this, ministers must act to ensure all care home and home care staff get the PPE they need and publish daily figures on deaths outside hospitals, including in care homes, so we know the full scale of the challenge we face.”