The 18-year-old, who was one of the most successful bowlers in this year's Indian Premier League, will become the first Afghan to feature at the tournament.
"I am very happy to have signed with the Strikers for the BBL," the leg-spinner said in a club statement.
"It is a huge honour to be a part of such a great tournament and even more of an honour to be the first Afghanistan player to participate on the BBL stage."
Adelaide Strikers coach Jason Gillespie hailed Rashid's signing as a "major coup".
"Rashid has set the world alight in T20 cricket with his energy, enthusiasm, and great control for a young guy," Gillespie said."He has some great variations, can bowl stump-to-stump and can be very hard to pick.
"We're delighted to be able to offer him the opportunity to play for the Adelaide Strikers."Rashid has claimed 63 wickets in 29 one-day internationals, including the fourth best figures in one-day history -- 7 for 18 against the West Indies in June.
He also became the first bowler to take a hat-trick in the T20 Caribbean Premier League, playing for the Guyana Amazon Warriors. The BBL season starts on December 20.