Voters approved tax increases to help pay for about half of a proposed 75,000-seat, retractable-roof stadium that will be among the league's largest, reports ESPN.com.
Pro-stadium campaign guru Rob Allyn called the victory "a historic moment for America's team and for the economy of the region".
Opponent Warren Norred said the vote was a victory for taking money from the people and giving it to Cowboys owner Jerry Jones.
The decision means the team will move to Arlington when its lease at Texas Stadium in Irving, where Dallas has played since 1971, expires in 2008.
The $650million stadium will be built next to the Texas Rangers' ballpark. Arlington is about 15 miles west of Dallas, but the team will still be called the Dallas Cowboys.
