Foster, 29, grabbed his chance in his first world title bout, stretching his winning streak to 10 in a row and taking his record to 20-2 with 11 knockouts.
"Man, it feels great," said the 29-year-old Foster, whose career was slowed by a four-month spell in prison five years ago. "This journey has been crazy."
Judges at the Alamodome in San Antonio, Texas, saw it clearly for Foster, whose speed and agility left Vargas groping.
Judge Tim Cheatham scored it 117-111, Alejandro Rochin saw it 119-109 and David Sutherland made it 116-112.
Foster said the victory came down to "dedication and hard work."
"I've got a great team around me," he said. "Just getting away from the distractions, getting myself mentally and physically right ... now, you know, I'm on top. It's crazy."
Mexico's Vargas fell to 36-1 with 22 wins inside the distance. The WBC super-bantamweight champion from 2017 to 2019, Vargas had captured the WBC featherweight title last July at the Alamodome with a split decision over Filipino Mark Magsayo.
