A former top aide at the United Auto Workers union pleaded guilty Wednesday to conspiracy charges, as part of a federal investigation into corruption within UAW leadership ranks that recently expanded to the union’s president and his predecessor.

Michael Grimes, a retired official who was assigned to the UAW’s General Motors Co. division and once served as an administrative assistant to a union vice president, stood accused of wire fraud and money laundering. Those charges carry a maximum of 20 years in prison. Under his plea...