The 21-year-old "The Fault In Our Stars" actor Elgort, will play financial genius Joe Hunt.
Egerton, 25, will portray tennis pro Dean Carney, reported Variety.
"We've loved this project from the moment we first read it. Now that it has this dynamic cast it's going to be something truly special. We couldn't be more excited to be a part of it," said executive producer Lemole.
The film will follow the true story of the rise and fall of two outsiders, whose investment pool propelled them into the upper echelons of Los Angeles in the early 1980s.