Health Secretary Matt Hancock confirmed 82 NHS and 16 social care workers had died so far during the outbreak.
He said he felt a "deep personal sense of duty that we must care for their loved ones".
Unions have welcomed the announcement, but called for the scheme to be applied to more sectors.
The Welsh government has promised the same payment to its NHS and social care staff while Scotland is finalising its own arrangements - although all devolved schemes will be paid for by the UK government.
The announcement comes ahead of a one minute's silence at 11:00 BST (10:00 GMT) on Tuesday to remember health workers who have died from the virus.
Prime Minister Boris Johnson will take part, along with others from across government.
Announcing the scheme at the daily government press briefing, Mr Hancock paid tribute to the "essential work" of NHS and social care staff.
He said: "Of course, nothing replaces the loss of a loved one.
"But we want to do everything we can to support families who are dealing with this grief."
The general secretary of the Royal College of Nursing, Donna Kinnair, said the new scheme would "bring reassurance to families in difficult situations".
She added: "No amount of cash can make up for a family member who passes away but financial security should never add to the worries of those in grief."
General secretary of Unison, Dave Prentis, also welcomed the move, saying: "Providing financial security for the families of all those who've paid the ultimate price for their professionalism and dedication is the very least we can do."
But the unions called for the scheme to be simple and quick, and to be open to more professionals, such as those working in primary care.
Labour welcomed the move but urged ministers to now "get a grip" on the supply of personal protective equipment to people on the frontline.
Liberal Democrat MP Layla Moran, who has been campaigning for such a scheme, said it was what NHS heroes "need and deserve".
But, she added: "Now, the government needs to go further. The scheme should include the families of all key workers - carers, teachers and bus drivers to name a few - who die on the frontline.
"The scheme should also match that given to the Armed Forces, covering pension benefits and funeral costs."
Mr Hancock said the government was looking into other groups of key workers and what schemes are already available to them.
There is no chance unless you take one