Bishop is 148-80-25 in 270 games with the Lightning, Kings, Ottawa Senators and St. Louis Blues.
The 30-year-old had a .910 save percentage and 2.54 goals-against average in 39 games this season. He has a .919 save percentage, 2.32 GAA and 19 shutouts in his NHL career and twice has finished in the top three in Vezina Trophy voting (second in 2015-16; third in 2013-14).
"He's an elite goalie in the NHL," Nill said. "His resume and track record speaks for itself. We think that he's an upgrade in net for us and I'm hoping he's a big part of our future moving forward."
Antti Niemi and Kari Lehtonen were the Stars goaltenders this season. Lehtonen was 22-25-7 with a 2.85 goals-against average and a .902 save percentage, and Niemi was 12-12-4 with a 3.30 GAA and .892 save percentage.
The Stars were 29th in the NHL in goals allowed per game (3.17) and 30th (last) in save percentage (.893).
The trade likely means Niemi and Lehtonen will be exposed in the NHL Expansion Draft that will supply the Vegas Golden Knights with their players. NHL teams can protect one goaltender and must submit their list of protected players by 5 p.m. ET June 17. Vegas must choose one player from each NHL roster.
Vegas also can sign any restricted or unrestricted free agent left unprotected by his team from June 18-20. These free agents would not otherwise be allowed to sign with a team different than the one they played for this season until July 1.
The announcement of the expansion draft selections will be made June 21 at the NHL Awards (7:30 p.m. ET; NBCSN, SN).
Bishop is coming off a two-year, $11.9 million contract he signed with Tampa Bay before the 2015-16 season. He was traded to the Kings with a fifth-round pick in the 2017 draft for goalie Peter Budaj, defenseman Erik Cernak, a seventh-round pick in the 2017 draft, and a conditional seventh-round pick in 2017.
The draft pick traded to Los Angeles was obtained by Dallas in a trade with the Montreal Canadiens for defenseman Jordie Benn.