The duo will fill the County's second overseas slot on what is effectively a job share arrangement.
Streak will join the County from mid-June until the end of August, when he will link up with the Zimbabwe squad ahead of the ICC Champions Trophy. Pretorious, who was at Durham last season, will play either side of Streak's stint.
The County's other overseas player, Australian Brad Hogg, is expected to play for most of the season.
Warwickshire captain Nick Knight said, "I am absolutely delighted that Heath will be joining us next season. "With 200 Test wickets to his name, he will help the young bowlers coming through as well as bolstering our batting line-up. His cricket experience will be invaluable."
Elliott to play for Glamorgan County