High performance manager Jamie Cox said securing the 24-year-old, whose unorthodox style helped Sri Lanka reach last month's World Twenty20 final, was a huge boost for his side.
"It was proven in the World Twenty20 that spin bowling has a massive part to play, and Ajantha was always our number one target," Cox said.
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"The shorter the game the more important it is to have a point of difference and he certainly provides that."
Mendis' huge variety of deliveries has left batsmen mystified since he emerged on the international scene last year and he has remarkable figures of 23 for 198 in his 10 Twenty20 internationals, with a strike rate of 9.9.
Other international stars playing in Australia's 'Big Bash' competition include Mendis' Sri Lanka team-mate Lasith Malinga, Shahid Afridi of Pakistan and West Indian pair Chris Gayle and Dwayne Bravo.
Cox said South Australia also hoped to sign retired Australian great Adam Gilchrist, although he conceded the big-hitting wicketkeeper was