Adams, who led the Sinn Fein party during much of the conflict in Northern Ireland, was among hundreds of people held by Britain without trial in the early 1970s under a policy meant to break the IRA. He has always denied membership of the militant group.
He was convicted in 1975 of twice attempting to escape from prison, but those convictions were quashed by the United Kingdom's Supreme Court three years ago.
The 74-year-old was refused compensation for his wrongful convictions by Northern Ireland's Department of Justice in 2021.
However, Judge Adrian Colton ruled on Friday that the decision was wrong and ordered the Department of Justice to reconsider Adams' application.
The judge said in a written ruling that the reversal of Adams' convictions "shows beyond reasonable doubt that there has been a miscarriage of justice".
The internment of suspected militants was one of the most controversial elements of the British counter-insurgency campaign.
Adams was initially detained in Belfast's Maze prison in 1973. On one of his attempts to flee, he switched places with a visitor at the prison who had been abducted while waiting at a bus stop, Belfast's High Court heard in 2018.
The UK Supreme Court ruled in 2020 that Adams was not lawfully detained as his internment was not approved by a British cabinet minister, meaning he was wrongly convicted of attempting to escape.
(Reporting by Sam Tobin; Editing by Toby Chopra)
