Pittsburgh received Brassard, Ottawa forward prospect Vincent Dunn, Vegas forward prospect Tobias Lindberg, and Ottawa's third-round pick in the 2018 NHL Draft.
[RELATED: 2017-18 NHL Trade Tracker]
Ottawa received Pittsburgh defenseman Ian Cole, goalie prospect Filip Gustavsson, its first-round pick in the 2018 draft, and its third-round pick in the 2019 NHL Draft.
Vegas received Pittsburgh forward Ryan Reaves and a fourth-round pick in the 2018 draft that belonged to the Vancouver Canucks. The Golden Knights will retain 40 percent of Brassard's remaining salary this season.
"This is the most complex trade I've made," Penguins general manager Jim Rutherford said. "Three-way deals are hard to make. We thought we had the deal made earlier in the day; it wasn't made. We had to make a couple changes. It took quite a bit longer than most. There was [salary] cap issues."
Brassard, a 30-year-old center, has 38 points (18 goals, 20 assists) in 58 games this season, the fourth of a five-year contract that has an average annual value of $5 million.
Video: The guys give an update on the Derick Brassard trade
"You look for a seamless fit," Rutherford said. "(Coach) Mike Sullivan knows him pretty well. He's anxious to come here. He's the type of player who will fit into our system very easily, so it should be pretty seamless."
Sullivan was an assistant for the New York Rangers in 2012-13 when Brassard joined them after being traded by the Columbus Blue Jackets.
The two-time defending Stanley Cup champion Penguins (36-22-4) lead the Metropolitan Division by one point over the Washington Capitals after defeating the Carolina Hurricanes 6-1 on Friday.
"We gave up a lot. But a lot of the things we gave up are futures, and our mandate is to win now," Rutherford said. "We can hang onto those futures and they can probably help three or four years down the line, but what we're trying to do now is win and put the best team out there. This deal gives us the best chance."
Selected by the Columbus Blue Jackets in the first round (No. 6) of the 2006 NHL Draft, Brassard has 420 points (159 goals, 261 assists) in 702 regular-season games during 11 seasons with the Blue Jackets, New York Rangers and Senators.
He has 55 points (22 goals, 33 assists) in 78 Stanley Cup Playoff games, including 11 points (four goals, seven assists) in 19 games for the Senators last season, when they reached Game 7 of the Eastern Conference Final and lost to the Penguins.
Cole had 13 points (three goals, 10 assists) in 47 games for Pittsburgh this season. He has 90 points (18 goals, 72 assists) in 385 games in eight seasons with the St. Louis Blues and Penguins, and 14 points (one goal, 13 assists) in 56 playoff games. He was part of Pittsburgh's Stanley Cup championship teams the past two seasons.
The 29-year-old is in the final season of a three-year contract with an average annual value of $2.1 million and can become an unrestricted free agent July 1.
Video: TBL@OTT: Brassard rips top-shelf one-timer for PPG
Gustavsson, 19, has a 2.16 goals-against average in 18 games with Lulea in the Swedish Hockey League, and had a 1.81 GAA and .924 save percentage in six games to help Sweden win the silver medal at the 2018 World Junior Championship, when he was named the tournament's best goaltender.
"In this deal we have acquired an elite goaltending prospect and a second first-round pick in June," Senators general manager Pierre Dorion said. "We feel that Gustavsson is one of the game's top goaltending prospects, a dynamic talent who has excelled in the Swedish Hockey League as a teenager and was the top goaltender at the most recent World Junior Championship. Ian Cole is a hard-nosed veteran defenseman who has a long pedigree of success, which includes two Stanley Cups."
The Penguins selected Gustavsson in the second round (No. 55) of the 2016 NHL Draft and signed him to a three-year entry-level contract June 16.
The Senators (21-29-10) have the third-fewest points in the NHL and are 13 points behind the Blue Jackets for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Reaves, a 31-year-old forward, had eight points (four goals, four assists) and 84 penalty minutes in 58 games in his first season with the Penguins. He played his first seven seasons for the Blues, when he had 51 points (27 goals, 24 assists) and 695 penalty minutes in 419 games. He had one goal in 36 playoff games with St. Louis.
"Ryan is a big, strong guy with some grit who brings some depth, and he can play," Vegas general manager George McPhee said. "The tough guys in this league, many of them have been ruled obsolete and they can't play, but this guy can play. …
"This is the kind of player most teams welcome, bringing in that kind of size (6-foot-1, 225 pounds) and grit. We thought it made sense what we did."
The Penguins received the Canucks' fourth-round pick in the trade that sent defenseman Derrick Pouliot to Vancouver on Oct. 3.
Vegas (41-16-4) leads the Pacific Division, Western Conference and NHL.
"We give up some [salary] cap space and a player to do this, and we get two assets that I feel really help the club," McPhee said.
Brassard addresses a need for a bottom-six center for Pittsburgh, which has Sidney Crosby and Evgeni Malkin as its top two. Malkin leads the Penguins with 73 points (34 goals, 39 assists) in 58 games; Crosby has 67 points (20 goals, 47 assists) in 61 games.
Nick Bonino was Pittsburgh's third-line center for their back-to-back Stanley Cup championships, when he was fourth on the Penguins in playoff scoring with 25 points (eight goals, 17 assists) in 45 games, including three game-winning goals. He signed as a free agent with the Nashville Predators on July 1.
"We've tried to get more depth at center and more insurance," Rutherford said. "Our centers have played pretty well, but you've got to have a lot of strength at center, and we just felt when we had a chance to get a guy like this it was a good addition."
Lindberg, 22, has 18 points (eight goals, 10 assists) in 48 games with Chicago of the American Hockey League. He was selected by the Senators in the fourth round (No. 102) of the 2013 NHL Draft.
Dunn, 22, has played this season with Belleville of the AHL and Brampton of the ECHL. He was selected by the Senators in the fifth round (No. 138) of the 2013 draft.