Adcock, 27, will share duties alongside the triple premiership player, who has been the sole leader since 2009.
Young midfielders Tom Rockliff and Daniel Rich have been named vice-captains.
Adcock is the eighth player in the history of the merged club to lead the team.
Coach Michael Voss said the new leadership model was a good fit for the Lions.
"Jed has demonstrated outstanding leadership over his time at the Lions, and most specifically in his past four seasons as a vice-captain," Voss said.
"As we know, 'Browny' won’t be around forever, and with Jed as co-captain, it will not only ease the load on 'Browny', but importantly they will both play a critical role in the continued development of Tom’s and Daniel’s leadership capabilities over the coming years.
"Jed is not only a leader on-field, he is an excellent representative of this footy club, and its culture and values."
Voss said it was a great honour for 22-year-old Rich and Rockliff to share duties as vice-captains.
"Tom and Daniel, as the deputies, are extremely capable young men who have shown maturity beyond their years in their short times at the club," he said.
Rockliff has been a deputy for the past two seasons, while Rich joins the leadership group for the first time.
The Lions play their first match of the year on Saturday in the first round of the NAB Cup against Gold Coast and Hawthorn at Metricon Stadium.
Jed Adcock is a defender in NAB AFL Fantasy. He averaged 81 points in 2012. Register your team at our AFL Fantasy Hub.
Michael Whiting covers Brisbane Lions news for AFL.com.au. Follow him on Twitter: @AFL_mikewhiting
