The Australian, who is managed by Ricky Hatton, was knocked down in the sixth round but floored Uzbekistan's Chagaev with a big right.
Browne, who improves his record to 24-0, followed up with a series of right hooks before the referee intervened.
Britain's Tyson Fury is considered the WBA's heavyweight 'super' champion as he also holds the WBO version.
In Birmingham, London's Bradley Skeete won a unanimous points decision to take the British & Commonwealth welterweight title from Sam Eggington.
Lucas Browne stopped defending champion Ruslan Chagaev in the 10th round to win the WBA heavyweight title in Russia.