Deadline confirms that Hamilton, who struggled with drug addiction following his initial breakthrough in 1999, has entrusted the rights to his life story to Affleck and producer Basil Iwanyk.
Affleck, who has also written the biopic's script, made his directorial debut with 2010 psuedo-documentary I'm Still Here, having previously starred in films including The Assassination of Jesse James by the Coward Robert Ford, and his brother Ben's first feature Gone Baby Gone.
Hamilton was chosen as first pick in the 1999 Major League Baseball Draft, but fell into alcohol and cocaine addiction after he was injured in a car accident.
After meeting his future wife in rehab, Hamilton eventually embraced religion and made his MLB comeback in 2007.
"[His life story] is tailor-made for a movie," said Iwanyk. "It has the mythic quality of The Natural, the faith-based angle of The Blind Side - and faith is a major part of our story - and the romance of Walk the Line.
"Casey has totally captured those elements in his take for the movie. It is an extraordinary odyssey that took him from the depths of drug addiction, estrangement from his family and suspension from baseball to a spectacular rebirth of his life, faith, marriage and major league career."
Affleck recently joined Rooney Mara and Ben Foster in contemporary Bonnie & Clyde thriller Ain't Them Bodies Saints.
Watch a trailer for I'm Still Here below: