Hastings was ruled out of the ninth edition of the Indian Premier League after an ankle injury last month.
Kolkata chief executive Venky Mysore confirmed Tait’s signing, posting an image of the veteran quick on Twitter on Wednesday.
"Pleasure to welcome @shaun_tait32 to @KKRiders family. Welcome Taity!," the tweet read.
Tait’s impressive form for the Hobart Hurricanes in the KFC Big Bash League saw him being named in the team of the tournament, in which he claimed 10 wickets, at 24.70, and consistently pushed the speed gun above the 145kph barrier.
He was named in Australia’s squad for the home series against India, but failed to seal a berth in the side for the ICC World T20 in India.
Tait previously played in the IPL for the now-suspended Rajasthan Royals, where he claimed 23 wickets, at an average of 27.82, in 21 matches.
KKR next face Rising Pune Supergiants at the Eden Gardens on Saturday.
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