The decision to resume racing was unanimously approved by the industry veterinary committee consulted by BHA, the authority said in a statement.
"Clearly, there is some risk associated with returning to racing. This risk has been assessed and, based on the evidence - and ensuring biosecurity measures are in place – the level of risk is viewed as acceptable," Brant said.
Last Thursday, the BHA cancelled all racing for the day after three cases of equine influenza were identified in vaccinated horses, and it later postponed racing in Britain until the middle of this week.
BHA said that as an additional measure, horses that have not been vaccinated in the previous six months will not be allowed to participate in the races.
Four positive tests for equine influenza were returned in horses in Newmarket on Sunday.
The equine influenza outbreak could not have come at a worse time, with the prestigious Cheltenham Festival only a month away. The four-day festival, the fourth most attended sporting event in Britain which attracts over 260,000 visitors, is due to start on March 12.
The event is worth about 100 million pounds to the local Gloucestershire economy.
(Reporting by Gaurika Juneja; Editing by Sandra Maler and Leslie Adler)