The Self Employed Income Support Scheme is designed to match the support being given to furloughed employees.
The grants will be calculated as 80% of average monthly profit over a period of up to three years.
The government said the money will be paid into the accounts of eligible people six days after applying.
The maximum payment will be £7,500, intended to cover March, April and May.
The scheme is the biggest direct financial support package for freelancers and the self-employed since lockdown started.
It was unveiled in March after the government faced criticism for failing to provide support for self-employed and freelance workers in its earlier package of economic measures.
Launching at 08:00 on Wednesday, the process will be run by HM Revenue & Customs, which has been operating and overseeing loan schemes and the government's furlough payments.
Those able to make a claim have already been contacted by HMRC and can use a unique reference to make their claim.
But those who started in business from early April last year will miss out, as will those who pay themselves just with dividends from a limited company.
Derek Cribb, chief executive of the Association of Independent Professionals and the Self-Employed, said: "For the self-employed, coronavirus is not only a health crisis, but also a pressing income crisis.
"We are delighted that the government has heeded much of IPSE's advice by setting up the Self-Employment Income Support Scheme, which extends a much-needed lifeline to those self-employed people who are eligible for it."
The government has not said whether the initiative will be extended into the autumn in line with the furlough scheme, which protects 80% of employees' wages up to £2,500 a month.
On Tuesday, Chancellor Rishi Sunak announced that scheme was being extended until the end of October.
Mr Sunak said: "With payments arriving before the end of this month, the self-employed across the UK will have money in their pockets to help them through these challenging times."
LONDON DAILY ARCHIVE
Self-employed grant scheme to open to applications
Millions of self-employed people whose business has been affected by coronavirus can apply for grants from the government from Wednesday.
13 May 2020 · 02:01 UTC
