Delport, who was born in South Africa but qualifies as a non-overseas player, has scored 2,045 T20 runs at an average of 25.56 with a strike rate of 135.70.
The 27-year-old left-hander played with elite performance director Andrew McDonald at Sydney Thunder in 2015.
McDonald said: "Cameron has experience in most of the world's top T20 competitions and his knowledge and skill will be valuable assets."
Delport shared the highest-ever one-day first-wicket stand with Morne van Wyk - an unbroken 367 set in a South African one-day game for Dolphins against Knights in Bloemfontein in October 2014.
Leicestershire's next match in the competition is against Lancashire at Old Trafford on Friday.
Leicestershire have recruited batsman Cameron Delport for the T20 Blast.