The panel filed the charges at the supreme court on Monday, bypassing the office of the attorney general after prosecutors declined to take part in the case.
"Now we just have to wait for the court to decide whether to take the case or to drop it. I do not know how long the court will take to announce its decision," Udom Faungfoong, the head of the investigation, said.
The charges centre on a procedural issue, claiming that Thaksin and his cabinet legalised the lottery with a decree, when they should have sought parliamentary approval, he said.
If the court accepts the case, Surapong Suebwonglee, the finance minister, and two junior ministers, would be required by law to step aside while the trial is conducted.
After taking power, the generals accused Thaksin of presiding over rampant corruption during his five years in power and the ASC has frozen nearly $2bn of Thaksin's assets in Thailand.
He will appear in court on Wednesday to face other corruption charges related to his wife's purchase of a piece of land in Bangkok from the Bank of Thailand.