Priestley, the chairman of JP Morgan Australia and New Zealand, had been a vice-president since 2022.
Sayers stepped down as president last month, after the AFL cleared him of posting a lewd image on social media.
The picture was posted on Sayers' X account, prompting an investigation by the AFL integrity unit. Sayers denied posting the image, saying his account had been hacked.
The Blues, who also cleared Sayers of wrongdoing, announced Sayers' resignation just minutes after the AFL had published the findings of their investigation.
Sayers' sudden departure prompted speculation about who would take over, with former federal treasurer Josh Frydenberg ruling himself out and former AFL chairman Mike Fitzpatrick also mentioned.
Priestley and fellow vice-president Patty Kinnersly had shared the top role since Sayers stood down.
"It is a privilege to receive this opportunity and not for a second will I take it for granted," Priestley said in a club statement.
"I can see the united culture our club is building, which is critical to our overarching goal of consistently contending and ultimately winning AFL and AFLW premierships."
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