The deal will be completed after Owens signs a free-agent contract with the Jazz next week - a step that is necessary to make the trade adhere to NBA salary requirements.
Free agents are not allowed to sign new contracts before July 12.
Fisher, the 24th pick in the 1996 draft, spent his first eight years in the league in Los Angeles with the Lakers. Signed as a free agent by Golden State in 2004, Fisher played the last two seasons with the Warriors.
Last year, he averaged 13.3 points and 4.3 assists while shooting 37.3 percent from the three-point line for a team that failed to reach the playoffs for the 12th straight year.
Fisher is probably best known for his game-winning shot in Game 5 of the 2004 Western Conference finals.
After San Antonio had taken a 73-72 lead in Tim Duncan's 18-foot jumper with 0.4 seconds remaining, the Lakers' Gary Payton inbounded the ball to Fisher.
In one motion, he caught the ball, turned and fired a 20-foot fallaway jump shot. It went in and, after TV replays confirmed he released the ball in time, the Lakers took a 3-2 lead in their series with the Spurs en route to the NBA Finals.