Marat Oganesyan, who served as deputy governor of Russia's second largest city from 2013 to 2015, was detained last year on suspicion of orchestrating a fraudulent deal worth 50.4 million rubles (£648,500) that was meant to provide the venue with a video display screen.
Investigators said that Oganesyan had admitted guilt as part of a pre-trial agreement.
"He fully acknowledged his guilt in the act for which he was incriminated, gave exhaustive evidence and took steps to repay the damage caused," the local branch of Russia's Investigative Committee said in a statement.
The decade-long construction of the Saint Petersburg stadium, which will host a World Cup semi-final next summer, has been plagued with spiralling costs and delays.
The pitch at the venue had to be hastily re-laid after it was cut up during the inaugural match there in April, raising questions about the venue's suitability to host Confederations Cup matches.
Prior to the problems with the grass, issues with the stadium's retractable pitch technology also caused the playing surface to vibrate, rendering it unfit for matches.
The venue, home to Russian football powerhouse Zenit St Petersburg, has also experienced issues with a leaking roof.
(Reporting by Gabrielle Tétrault-Farber; editing by Amlan Chakraborty)
