Indianapolis-based Republic Airways Holdings is a regional carrier that currently flies under contract for other airlines. Midwest is based in Milwaukee and had been owned by private equity firm TPG Capital.
Republic Airways Holdings said Friday that Midwest will continue to operate as a branded carrier.
Republic Airways Holdings also has made a bid to buy the parent of Frontier Airlines, which is operating under bankruptcy protection. While a court has approved that deal, Southwest Airlines recently made a rival bid for Frontier. An auction is expected to be held in August.