Lawler, who is senior vice president of international and deep-water operations at Anadarko Petroleum, will join Chesapeake on June 17, the company said.
McClendon's departure on April 1 came after a tumultuous year in which a series of Reuters investigations led to civil and criminal probes of the second-largest U.S. natural gas producer. Chief Operating Officer Steven Dixon had been appointed as interim CEO.
McClendon's exit was announced in late January, after a governance crisis and a liquidity crunch due to heavy spending on oil and gas properties.
Big shareholders took control of the board last June after McClendon was stripped of his title as chairman of the company he co-founded in 1989.
Chesapeake said on Monday the chairman position will be discontinued and Archie Dunham, Steven Dixon and Domenic Dell'Osso Jr. will continue to serve in their roles as non-executive Chairman of the Board.