A former British intelligence officer who is now a director of a private security-and-investigations firm has been identified as the author of the dossier of unverified allegations about President-elect Donald Trump’s activities and connections in Russia, people familiar with the matter say.

Christopher Steele, a director of London-based Orbis Business Intelligence Ltd., prepared the dossier, the people said. The document, which an official close to the matter said was prepared under contract to both Republican and Democratic adversaries of Mr. Trump, alleges that the Kremlin colluded with Mr. Trump’s presidential campaign and claims that Russian officials have compromising evidence of Mr. Trump’s behavior that could be used to blackmail him.

Mr. Trump has dismissed the dossier’s contents as false and Russia has denied the claims.

Mr. Steele, 52 years old, is one of two directors of the firm, along with Christopher Burrows, 58.