The 33-year-old will be available for three T20 Blast matches, against Kent, Middlesex and Glamorgan.
Kulasekara has taken 56 wickets in 50 T20 internationals for Sri Lanka and has also played 21 Test matches and 173 one day internationals.
Meanwhile, Bangladesh bowler Mustafizur Rahman is now due to join Sussex for their final four T20 Blast group games.
The 20-year-old’s move to Hove has been delayed by his commitments with Indian Premier League side Sunrisers Hyderabad.
In the meantime, Sussex fast bowler Chris Jordan has been made available for Thursday night’s T20 Blast match against Kent, having been released from the England ODI series with Sri Lanka. (Courtesy BBC Sport)