The former Origin Energy managing director retired from that role last month after about 16 years in the job, the ABC reported.
Livingstone said King's tenure at Origin qualified him well for leading the lobby group for Australia's biggest businesses.
"Grant's leadership at Origin Energy in delivering the APLNG project, one of Australia's largest ever capital projects, is an example of the wealth of experience he brings to the role," she said.
King will take over as BCA president effective from the organisation's annual general meeting on November 17.
"My focus will be on continuing to drive a more innovative and competitive economy, improving incentives for businesses to invest, and making the economy more flexible so it can respond to global forces of change," King said.