A federal jury found John Rowland Mills guilty on the nine counts in July. His sentencing is set for next Tuesday.
U.S. District Judge James Teilborg on Friday threw out all but one of the convictions.
Teilborg said in a written order that the eight wire transfers were not necessary for the long-term perpetration of the fraud but instead were for personal expenses and investments.
Mills embezzled from then-House Speaker Jim Weiers' 2008 re-election campaign account but returned it just before the election. The conviction for that final wire transfer stands.
Mills worked for majority House Republicans before resigning in May 2012.