Dallas sent a fourth-round pick in the 2017 draft to Los Angeles for Bishop, a pending unrestricted free agent. The Stars will have the first shot at signing Bishop before free agency starts July 1.
"Ben has proven that he is one of the elite goaltenders in the NHL," Stars general manager Jim Nill said in a statement. "This offers us the opportunity to negotiate with him before the free agency period begins."
The fourth-round pick is the 114th overall. Dallas acquired it when Jordie Benn was traded to Montreal last season.
Bishop, 30, was 2-3-2 with a 2.49 goals-against average with the Kings and 18-15-5 with a 2.54 GAA overall last season.
After a slow start to his NHL career in St. Louis and Ottawa, the 6-foot-7 Bishop had been an above-average starter for the past four seasons in Tampa Bay. He is a three-time All-Star and was the runner-up for the Vezina Trophy in 2015-16.
He backstopped the Lightning to the 2015 Stanley Cup finals, where they lost to the Chicago Blackhawks. But Andrei Vasilevskiy has been the Lightning's goalie of the future for the past several seasons, and the 22-year-old Russian is expected to be protected by Tampa Bay in the expansion draft.
The Stars fell from being the top team in the Western Conference in 2015-16 to missing the playoffs this season, and goaltending played a big part. Kari Lehtonen was 22-25-7 with a 2.85 GAA, and Antti Niemi was 12-12-4 with a 3.30 GAA. Only Colorado had a worse GAA as a team.
But it won't be cheap to sign Bishop. He'll be looking for a long-term deal, and Lehtonen and Niemi are both under contract for one more season at $5.9 million and $4.5 million, respectively. A buyout for one could be in the works.
Carolina worked a similar trade this offseason, acquiring the rights to Blackhawks goalie Scott Darling and then signing him to a four-year deal.
Information from The Associated Press was used in this report.