Gayle joined Sydney Thunder after the Perth Scorchers rejected his contractual demands, the Western Australia Cricket Association said.
Gayle, 31, has an outstanding T20 record and averages 32.46 in T20 internationals for the West Indies with a strike rate of 144.49.
He finished this year's Indian Premier League season as the highest run-scorer in the tournament for the Bangalore Royal Challengers.
"I am thrilled to be able to come to Sydney and play for the Thunder," Gayle said in a statement.
"Having worked well with (coach) John Dyson in the West Indies, I was impressed with his plans for the Thunder and I think the team will have a great chance to win this competition.
"I look forward to walking out to open the batting with David Warner when the season starts."
The WACA said it made an offer of AUS$250,000 (US$265,000) to Gayle through his management company.
WACA chief executive Graeme Wood said it was disappointing to lose Gayle after he had played for the WA Warriors in the past two Big Bash competitions.The Big Bash T20 tournament runs from December 30 to February 5.Details of Gayle's Sydney Thunder offer were not disclosed.