Jamaican Bolt, who won three golds at last year's London Games, had not previously raced in the United Kingdom since 2009 because of tax rules which would have left him out of pocket.
"The Government is determined to do everything possible to secure the Olympic legacy and I am delighted to grant this exemption," the Chancellor of the Exchequer, George Osborne, told Thursday's Daily Telegraph.
The London meeting, switched from its traditional Crystal Palace home to the Olympic Stadium to mark the first anniversary of the Games on July 27, is expected to be a 80,000 sell-out and would have been damaged by the absence of athletes such as Bolt.
British tax rules mean that visiting overseas athletes would have paid tax on their earnings from the meeting but also on part of their global income including sponsorship deals.
Despite Osborne's intervention, Bolt has yet to confirm his attendance.
"I think it's about two weeks before the World Championships (in Moscow), which is quite late, but it's London and it's the Olympic Stadium again so it obviously has an attraction," his agent Ricky Simms said.