Yunus Rahmatullah was detained by British forces in 2004 in Iraq, where he said he was with a friend who was on a pilgrimage.
He was transferred into US custody in Afghanistan and held for 10 years without charge before being released this year, and currently lives in Pakistan.
Rahmatullah alleges that he was subjected to torture while in detention, including being beaten on the soles of his feet with rubber flex, being exposed to tear gas and being immersed upside down in water tanks.
The British defence ministry had argued that the case could not be heard as British courts did not have jurisdiction over the actions of US forces.
But judge George Legatt said in his ruling that for a British court to refuse to hear a case on those grounds "would seem to me to be an abdication of its constitutional function".
The judgment, which was published by the British justice ministry, also concerns claims made by three Iraqi civilians of abuse by British soldiers in Iraq before they were handed over to US forces.
"It is now high time for the British government to abandon its attempts to evade judicial scrutiny of its conduct in operations involving the US in Iraq and Afghanistan, so that justice may finally be served," said Sapna Malik, Rahmatullah's lawyer.
The decision comes after a British court last month issued a similar ruling in a separate case saying that a Libyan politician can sue the government over his claim that Britain conspired with the CIA in his "rendition" to Libya for torture.
British officials had pursued the same defence of claiming that the US involvement meant the case could not be heard by British courts.
The judgment in Abdul-Hakim Belhaj's favour said that "unless the English courts are able to exercise jurisdiction in this case, these very grave allegations against the executive will never be subjected to judicial investigation".
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This is due to our judiciary and transparency, which we thrive on in UK. Nothing special, it could have been any nationality, it would have made no difference. This is called system, which we taxpayers and subjects of UK are proud to withhold, without compromise.