In a criminal case at Inner London Crown Court, Howard Hill, Richard Michael Forrest and Lee Stewart accepted their guilt and will be sentenced next month.
Following the Olympics and before West Ham were granted use of the stadium, football club Tottenham was accused by the Olympic Park Legacy Company (OPLC) of ordering surveillance by private investigators on board members tasked with deciding the fate of the arena after the Games.
Accountancy firm PKF was employed by Tottenham who denied being involved in illegal activity.
Hill, a former partner at PKF, was accused of unlawfully obtaining personal data such as phone bills and bank statements from West Ham and OPLC workers.
At a separate court case, PKF was accused of unlawfully obtaining telephone records of West Ham's vice-chairman Karren Brady during the bidding process.
After much wrangling and many meetings, West Ham agreed on a 99-year deal to move from Upton Park and rent the revamped £486m stadium.
The 80,000-seat venue will be downsized to 54,000 and reconfigured with a new roof and retractable seats.
As the anchor tenant, West Ham will have primary of use of the stadium, although the venue will retain the running track and stage other sporting events and concerts.