Burwell's departure comes with immediate effect and follows a summer in which Sunderland have faced criticism over ticketing, membership and communication issues despite their progress on the pitch.
Louis-Dreyfus will work closely with the club's management team and assume responsibility for the executive chairman role as Sunderland prepare for their return to European competition.
Burwell was appointed interim chief executive earlier this year after replacing David Bruce. His brief included overseeing a wide range of club operations and working alongside director of football Florent Ghisolfi during the summer transfer window.
The change in the boardroom comes only days after Burwell addressed supporters' concerns and committed to tackling problems surrounding the club's off-field operations.
Those concerns were raised during a meeting with Sunderland's supporter collective, where fans criticised the introduction of a new membership scheme and the migration of online accounts.
A statement from the Red and White Army highlighted problems with supporters logging in, resetting passwords, accessing purchase histories and viewing Black Cat Points. It also criticised queues at the stadium after online and telephone support failed to cope with demand.
The group said the membership scheme had been poorly communicated and had left some supporters paying an additional £48 for tickets that were more expensive and less desirable than those available to fans who waited to purchase them.
The supporters also warned that the issues needed to be resolved urgently with Europa League fixtures creating significantly higher demand for tickets.
Burwell accepted the statement and acknowledged that Sunderland had work to do to rebuild trust with supporters. Meeting minutes said he recognised that the pace of improvement had not been fast enough, while also pointing to the club's recovery from a decade ago.
The club also acknowledged that its customer service team was stretched and that a more digital approach would be needed to help supporters receive answers more quickly.
Sunderland have made significant progress on the pitch since returning to the Premier League, but the latest change places renewed focus on the club's off-field operation.
Louis-Dreyfus will now lead that work alongside the senior management team, with Sunderland yet to announce a permanent replacement for Burwell.