The move follows years of campaigning by the family of Mahmood Mattan, in particular his widow Laura.
Mattan, a Somali seaman from the Tiger Bay area of Cardiff, was hanged in 1952 for the murder of Lily Volpert. Mrs Mattan's solicitors said yesterday that it is "beyond belief" that Mr Mattan was executed.
Miss Volpert, a shopkeeper, was found with her throat cut and between pounds 100 and pounds 200 was missing. Mattan's trial lasted three days and the jury was out for little more than 90 minutes. He was executed seven weeks after his conviction.
He was convicted on the identification evidence of one witness and one piece of "forensic" evidence: blood on one shoe. The witness maintained that Mattan had left the shop at 8pm at the latest. But even Miss Volpert's family were sure that she was still alive at 8.05 to 8.10pm. The man was described as being 5ft 10in, with a gold tooth, no hat or coat, aged 30 to 40 and wearing a brown suit. Mattan was 5ft 8in and aged 29. He had no gold tooth and had worn a dark overcoat that night.
The blood was a few tiny specks on a secondhand shoe. It was not tested forensically.
The Criminal Cases Review Commission has referred the case to the Court of Appeal which could posthumously clear Mattan of the murder.