Thorburn is currently leading the review of the Bombers' football operations and will take over as CEO on November 1.
The 57-year-old, who was chief executive of NAB from 2014 to 2019, was also a member of the panel that selected Brad Scott as senior coach.
Thorburn fills the role vacated by Xavier Campbell, who resigned in August amid a period of off-field upheaval.
Campbell's exit came after a difference of opinion with new president Dave Barham over former coach Ben Rutten's sacking.
Barham ousted former president Paul Brasher earlier that month.
In a letter to Bombers members on Monday, Barham described Thorburn's appointment as "a significant step forward for the club".
"In Andrew, we have secured a highly credentialed leader, with a proven track record in development and building the leadership capabilities of his people," Barham wrote.
"Andrew's focus will be on running Essendon like a club, with a renewed focus on our members and the core reason for which we exist – football.
"Our recent appointments of Brad Scott and today with Andrew, demonstrate our commitment to leadership and providing the right environment to ensure we achieve sustained success as a club."
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