The 25-year old replaces Afghanistan leg-spinner Qais Ahmed. In 52 T20 matches Green has scored 374 runs and taken 40 wickets.
Green will be available for the entire tournament as a Silver category player on the Multan Sultans team roster.
Green has previously represented Lahore Qalandars in the second and third season of Pakistan Super League. The Australian was recently part of the Sydney Thunder squad in Big Bash and also captain the CPL side Guyana Amazon Warriors to the final of the 2018 edition of Caribbean Premier League.