The man’s past crime will be “delisted” from the search engine after a “groundbreaking and “unprecedented” High Court ruling.
The man, named only as NT2 in court, wanted a past crime he committed to not come up in search results.
Mr Justice Warby delivered a blow to Google by ruling in his favour on Friday.
The judge rejected a similar claim by a second businessman, referred to only as NT1, who had been convicted of a more serious crime.
The claims were apparently the first of their kind in England.
Carter-Ruck, the law firm which acted for both men, described the cases as “unprecedented” and “groundbreaking”.
Google contested the two claims, which were heard in separate High Court trials in London.
Both businessmen, who cannot be named for legal reasons, were convicted of crimes many years ago.
They argued their convictions were now legally “spent” and they had both been rehabilitated.