Rogers, 83, a Democrat from Birmingham since 1982, admitted guilt in a kickback scheme diverting community project funds.
In his plea deal, Rogers agreed to resign, recognizing his ineligibility with a felony conviction.
Federal prosecutors suggest 14 months of home confinement and a $197,950 restitution for Rogers.
Former Rep. Fred L. Plump, Jr. and Rogers' ex-assistant, Varrie Johnson Kindall, also admitted guilt in the scheme.
A special election will fill Rogers' House seat, making him the third lawmaker in this term to plead guilty to a criminal charge.
Prosecutors allege Rogers directed $400,000 to a youth sports organization, receiving $200,000 back.
Another ex-lawmaker, David Cole, previously pleaded guilty to voter fraud in a separate case.