Heughan joins a cast that includes Bodyguard star Keeley Hawes as Neal and Downton Abbey star Hugh Bonneville as Dahl.
Neal starred with Newman in 1963's Hud , which earned her an Oscar and Newman an Oscar nomination.
The yet untitled biopic takes place in the early 1960s as Dahl and Neal went to the English countryside to raise their family and their relationship is put to the test by tragic events, Deadline reported.
John Hay (Lost Christmas) is directing the film.
"We are delighted that Sam has joined us. He is the perfect actor to play Paul Newman and a terrific addition to our already wonderful cast," producer Donall McCusker said in a statement.
Neal, who died in 2010 at age 84, was also known for starring in The Day the Earth Stood Still and Breakfast at Tiffany's. Dahl, who died in 1990 at age 74, famously wrote Charlie and the Chocolate Factory, James and the Giant Peach, Matilda, The Witches, Fantastic Mr. Fox and The BFG.
The couple divorced in 1983 after 30 years of marriage.
Newman died in 2008 at age 83. He starred in films such as Cool Hand Luke, Butch Cassidy and the Sundance Kid and Slap Shot.
Heughan is best known for portraying Jamie Fraser on Outlander. The series will return to Starz for Season 5 on Feb. 16.
"It's been an amazing journey. You know, I never thought when I first got the job that we would still be here. But it's a great show and this season I think is probably stronger than last season," he told host Jimmy Fallon.