Kelly is slated to join the KKR squad before their next home game against Chennai Super Kings on Sunday.
The 24-year-old Kelly, a right-arm pace bowler, has played 16 First-Class matches, five List A games and 12 T20s so far and has not featured in the past editions of the IPL, the franchise said in a statement.
Highly rated in Australia, Kelly is expected to add value to KKR squad. Former Australian chairman of selectors Mark Waugh had said Kelly "could do the job for Australia" at the World Cup if any of their first-choice picks didn't recover from injuries.
KKR are currently at No. 2 in the points table after losing their last match against Chennai Super Kings at Chennai. But the two-time champions would be hoping to avenge the loss when they take on the Men in Yellow at their own backyard on Sunday.