Brady's mobile phone records were obtained during an investigation which centred around the bidding process for the Olympic Stadium.
Tottenham asked the firm PKF to investigate that process.
Howard Hill, Richard Forrest and Lee Stewart all pleaded guilty on 8 November to illegally obtaining confidential information on West Ham directors and officials from the Olympic Park Legacy Company.
Tottenham strongly deny any claims of spying and it was said in court one of the investigators had told the club he did not believe he had been acting illegally.
Hill was fined £100,000 as the main investigator, with Judge McCreath saying: "You had full control over this project. You engaged others to do your dirty work for you."
Stewart was fined £13,250. The judge said his involvement was limited to two of the victims.
Forrest was fined £10,000. The judge said, like Stewart, he had acted on Hill's instructions.
As well as Brady, victims included fellow joint-chairman David Sullivan and Ian Tomkins of West Ham, along with a number of Olympic officials and the Mayor of Newham, Sir Robin Wales.
David Gold, another joint-chairman of the Hammers, was named as someone who became the focus of attention.