Adcock, 28, was on Thursday unveiled as the sole Lions skipper after sharing the role with Brown last season.
Midfielder Tom Rockliff, 23, will be Adcock's deputy while Daniel Rich, Joel Patfull and Daniel Merrett have been appointed deputy vice-captains.
Leppitsch said Brown, 32, may have taken a step back ahead of his 15th AFL season but would still play a major role.
"He was really keen to step away and become a mentor and we were keen to do the same thing," Leppitsch said.
"I think it'll help him personally but more importantly it'll help our club develop new leaders.
"If Browny is always in those meetings, he'll always be heard, he's always dominant with a strong personality - I think it's time the next generation came through.
"We're really conscious to use his strengths but also grow others from underneath."
Brown backed the new-look hierarchy under incoming coach Leppitsch which was finalised at a recent pre-season leadership camp on the Sunshine Coast.
"Obviously I have relished my time as captain, but I think it's the right time for a changing of the guard," said Brown.
"I'm coming towards the end of my career and I think with Leppa on board it's the perfect time for a fresh start.
"I'll still be there to support the boys when they need but I have every confidence in the ability of Jed, Tom and our next generation of leaders to take the club forward."
The rest of the Lions leadership group consists of Pearce Hanley, Matthew Leuenberger, Dayne Zorko, Jack Redden and Mitch Golby.
Leppitsch said the captaincy would be reviewed each year but believed Adcock - a veteran of 163 games - was currently the right man for the job.
Adcock had a taste of what to expect when he captained the Lions by himself for the last four games of the 2013 season when Brown was sidelined with a foot complaint.
"This won't be the biggest change. I would have thought the implementation of a new gameplan and adapting to things on-field will be our biggest challenge," Leppitsch said.