It remains unclear whether the investment amounts to a direct takeover of the club.
Tomlins told the BBC that the irregular payments were made through the club's holding company J10.
A Luton statement said: "Earlier this year Mr Tomlins approached the FA requesting a meeting to clarify certain matters relating to the football club.
"Following this meeting the FA is currently carrying out an inquiry."
Tomlins said: "There has been too much disruption surrounding the club in recent months. I feel it is appropriate for me to stand down at this time."
The Luton statement added: "The board recognises the contribution made by Mr Tomlins while he was chairman of the club.
"As the matter is now with the Football Association there will be no further comment by the club until the inquiry has been completed."