Brown was pick No.15 in the 2008 national draft, but the key-position player managed just 15 games for the Cats after struggling with injury early in his career.
Brown played in the Cats' 2012 VFL premiership team and booted 98 goals in 63 VFL games for Geelong.
Key-position player Hamling did not manage a senior game in three seasons at Simonds Stadium after being taken at pick No.32 in the 2011 national draft.
The West Australian played 42 VFL games for the Cats and finished third in their VFL best and fairest this year.
"We thank Taylor, Mitch and Joel for their efforts over their time at the club and wish them every success in their future endeavours," Geelong football manager Neil Balme said.