Doedee has been in the Crows' leadership group for the past four years and was at one stage considered a future club captain, but is on the move after a season cut short by injury.
The 26-year-old ruptured the anterior cruciate ligament in his right knee in June and will be out of action for the first half of the 2024 season.
Doedee, who sustained a similar injury in his left knee in 2019, has played 82 games for Adelaide over six years.
In a statement on Wednesday, Brisbane confirmed Doedee had signalled his desire to join the club.
"The Lions will now work with the Crows to acquire Doedee via the AFL free agency process," the club said.
Doedee's status as a restricted free agent means Adelaide have the option to match the Lions' contract offer, potentially forcing them into a trade.
If not, the Crows would likely receive a second-round draft pick as compensation for losing Doedee through free agency.
Doedee had also attracted some interest from Collingwood, who beat the Lions in last weekend's grand final.
In a statement, Adelaide list boss Justin Reid said the club would assess its options in order to secure the best possible outcome during the free agency window.
The window starts on Friday and runs until October 13, while the trade period is open from October 9 to 18.
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