Smith, who admitted to pre-meditated ball tampering in the Cape Town Test against South Africa, was handed a 12-month ban by Cricket Australia and subsequently, BCCI barred him from participating in the upcoming edition of the IPL, starting April 7.
The Royals then announced Ajinkya Rahane as their captain for IPL 2018.
Klaasen, who made his international debut against India earlier in the home season, showed his clean-hitting abilities in the four ODIs and three T20Is.
The 26-year-old Klaasen was picked up for Rs 50 lakh from the Registered and Available Player Pool (RAPP) list, the BCCI announced.
Commenting on the development, Head of Cricket of Rajasthan Royals Zubin Bharucha said: "We are delighted to have Klaasen onboard. His hard hitting ability with plenty of options against spin makes him dangerous through the middle of an innings."
"What struck us about Klaasen other than his ability to strike a ball was his inherent hunger to make every opportunity count, this is a good space to be in as a cricketer and batsman. We look forward to working with Klaasen to ensure he has a great career in the IPL," added Bharucha.
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