Former director of engineering Jason Mahoney will be the new COO while Stuart Kennedy, previously director of people at IAG Cargo, will replace Williams, a BA spokeswoman said in an emailed statement.
Goersch has decided to move back to North America and Williams plans to leave in the next few months, the company said.
British Airways executives have also had a tumultuous year, dealing with a pay dispute that resulted in the first pilot walkout in the airline's history.
The airline's owner IAG has seen a number of managerial changes - long-time Chief Executive Willie Walsh is stepping down in March to be replaced by Iberia chief Luis Gallego.
(Reporting by Akshay Balan and Rama Venkat in Bengaluru)