The case was brought by businesswoman Gina Miller, who argued the move was “an unlawful abuse of power”.
Rejecting Ms Miller’s case, Lord Justice Burnett said she could immediately appeal because of the important points of law at stake.
The appeal is expected to be heard at the Supreme Court on 17 September.
A similar legal challenge heard at Edinburgh’s Court of Session on Wednesday also failed.
The prime minister announced on 28 August he wanted to shut down Parliament, a process known as proroguing, for five weeks ahead of a Queen’s Speech on 14 October.
His political opponents argued Mr Johnson’s aim was to avoid parliamentary scrutiny and to stop them passing legislation that would prevent the UK leaving the European Union without a deal on 31 October.
The UK government insisted this was not the case, and said proroguing Parliament would allow Mr Johnson to set out his legislative plans in the Queen’s Speech while still allowing sufficient time for MPs to debate Brexit.