The 21-year-old Sushant, who hails from Ranchi, has played four first-class matches, snaring 13 wickets.
UP medium pacer Dubey has a back injury and has been ruled out for the rest of the tournament, the IPL said in a release on Wednesday.
Dubey hasn’t featured in a single match for SRH this season.
Sushant will join SRH at the price of Rs 20 lakh.
SRH sit fourth on the points table, having won five of their nine matches.
They will take on the Delhi Capitals on Thursday at the Brabourne Stadium on Thursday.