He will be with the Hurricanes throughout the tournament, which runs from December to early February.
Jacks join a raft of English players at the tournament with – among others – Jonny Bairstow turning out for Melbourne Stars, Dawid Malan at Hurricanes and Jason Roy at Perth Scorchers.
There is more to come yet, with Nottinghamshire’s Joe Clarke set to stand in for Roy while he tours South Africa with England.
Essex’s Lawrence, meanwhile, has signed up with Brisbane Heat as a replacement for another Englishman, Tom Banton, while he is in South Africa.
Lewis Gregory is also on Heat’s books. Lawrence, 23, bats in the middle order and bowls handy all-sorts spin.