The cable network made the announcement on Friday.
Gadot had been rumored as the leading candidate for the role for about a year.
The Israeli actress and her husband, Yaron Varsano, will also serve as executive producers of the still-untitled series alongside a team including Sarah Treem, Warren Littlefield and Katie Robbins.
“The life of Hedy Lamarr was a truly fascinating one. She stood at the forefront of many issues that challenge women and our society today,” Showtime’s president of entertainment, Jana Winograde, said in a statement. “In Gal Gadot, we have found the transcendent actress to portray the deeply complex Lamarr.”
Lamarr is best known as a beautiful Hollywood star, having acted in films such as “Algiers” (1938), “Boom Town” (1940), “I Take This Woman” (1940), “Come Live With Me” (1941) and “Samson and Delilah” (1949).
But she was also credited with creating a prototype for a frequency-hopping signal during World War II that could help the Allies disrupt radio-controlled torpedoes. Later versions of the system were used in the creation of Bluetooth and Wi-Fi.
Lamarr was born Hedwig Eva Maria Kiesler in Austria, the daughter of a Ukrainian Jewish father and a mother from an upper-class Jewish family in Budapest, though her mother converted to Catholicism.