The new pay rates for thousands of its staff will take effect from the start of the New Year, the company said.
Sports Direct - which is controlled by wealthy businessman Mike Ashley - said it would cost £10m a year.
But the Unite trade union accused the company of a "PR stunt" and of "gulag" working conditions at its headquarters.
The retailer came under pressure earlier this year for effectively not paying its staff the full minimum wage.
It insisted on searching employees at the end of their shifts, which they were not paid for.
That extra time meant the average hourly rate was as low as £6.50 an hour, instead of the national minimum wage of £6.70.
"We have a responsibility to set a high moral standard," said Mike Ashley in an interview in the Daily Mirror.
"I want to see Sports Direct become the best High Street retail employer after John Lewis," he said.
However, the Unite trade union, which represents warehouse staff at Sports Direct, accused him of a PR stunt.
"This pitiful promise by Sports Direct to pay just over the minimum wage should not distract from the 'Victorian' work practices at the retailer's massive Shirebrook depot," said Unite regional officer Luke Primarolo.
"Nor should it deter HMRC from investigating the possible non-payment of the minimum wage to the thousands of agency staff who eke out a living on the site."
In his interview, Mike Ashley said that workers over 21 will now earn "around" £6.85 an hour.
When the new National Living Wage of £7.20 comes into effect in April 2016, staff over 21 will earn £7.35.
Shareholders, including Royal London Asset Management, were among those who criticised the company, alongside the TUC and politicians.
The former shadow business secretary, Chuka Umunna, called the retailer "a bad advert for British business".
Shares in the company fell by more than 10% on 10 December, in the wake of the criticism.
News of the pay re-think sent Sports Direct shares up by more than 1% in morning trading on Thursday.
Earlier in the year staff members told the BBC Inside Out programme that they were too frightened to take sick days, for fear of losing their jobs.
But the company denied the accusation, saying staff who failed to reach performance targets were offered support and training.
The retailer Sports Direct has announced that it will pay its staff more than the minimum wage, following criticism of its employment practices.