The stars were also sentenced to 40 hours community service and also received a fine, while all charges were dropped against the rest of the family.
In an exclusive statement, Billy says the family is ready to put the troubles behind them.
“Alaska’s dividend program has specific requirements for the length of time in the state, and the reasons for being out of Alaska. Because of the way we live our lives and the way we often unconventionally travel, I didn’t keep good track of our movements,” Billy tells PEOPLE in a statement. “I accept full responsibility for filing for benefits without confirming that we met the requirements. We are committed to living in Alaska for the long term and we respect the state’s rules. I thought it best to settle to put this behind us.”
Alaskan Bush People network Discovery is not commenting.
Billy, 63, and Joshua, 32, claimed to have been living in Alaska from 2009 to 2012, when they were actually living in Seattle during that time. In a plea deal submitted in November, Billy admitted that he “stole $7,956 from the people of Alaska.”
Alaska divides oil dividend payments equally among its residents, with the judge in the case estimating each of the state’s residents were deprived of about three cents each because of the payments made to the Browns.