They said it was treating claims made by the newspaper "with the utmost seriousness" and insisted it was "certain of the robustness" of its successful bid.
The Olympic Park Legacy Company (OPLC) board, in charge of securing the future of the Olympic Park site, voted 14-0 in February to make the Hammers the first choice to move into the £486million stadium.
In a statement released on their website, the club announced: 'West Ham United can confirm the club are taking legal action in relation to allegations made in today's Sunday Times.
'We are certain of the robustness of our successful bid for the Olympic Stadium. The newspaper's statement that Tottenham Hotspur employed the
investigators who obtained private information illegally is one we are treating with the utmost seriousness and no doubt data protection and prosecution agencies may also do so.
'The only wrongdoing here is by those who have broken the law and obtained private information. It would appear that no stone has gone unturned trying to find a way to undermine our bid including apparently targeting the 14 Olympic Park Legacy Company (OPLC) Board members who had voted unanimously on the bid in our favour.
'The suggestion of 'secret cash' in the Sunday Times article is absolutely and categorically denied. As such, legal action is being taken against the Sunday Times, as well as Tottenham Hotspur.'