"An investigation was launched in August 2011 by officers from the Economic and Specialist Crime Command following allegations by West Ham and the Olympic Park Legacy Company in respect of the unlawful obtaining of information," a Metropolitan Police statement said on Tuesday.
"A 29-year-old man was arrested in connection with the investigation. He was arrested at an address in Sussex on suspicion of fraud offences and has been taken into custody at a Sussex police station, where he remains."
West Ham were chosen as the preferred long-term tenants of the 500-million-pound stadium in February.
Tottenham, who said a 40-million-pound loan from bid partner Newham Council gave West Ham an unfair economic advantage and made the decision unlawful, dropped their request for a judicial review after the deal to award the stadium to West Ham fell through last month.
West Ham and Tottenham became involved in a war of words before and after the initial decision and the OPLC chairwoman Baroness Ford said the 14 board members who made the decision had been put under surveillance by Tottenham.
Speaking to the London Assembly, she said: "My board were put under surveillance by Tottenham Hotspur and the chairman of Tottenham Hotspur felt confident enough to say that in the Sunday Times several months ago, that all 14 members of my board were put under surveillance.
"The Metropolitan Police are now conducting an investigation into that surveillance. There has been all kinds of behaviour here that I could not have anticipated which, believe me, has not been pleasant in the last 12 months."
Tottenham strongly denied any suggestion that it had carried out surveillance on executives at West Ham or the OPLC.
"The club did not undertake, or instruct or engage any party to conduct surveillance on any member of the OPLC committee whatsoever and we consider the making of this baseless accusation to be wholly inappropriate and irresponsible," a club statement said.
"We totally reject this accusation in the strongest possible terms."
