The Stars also acquired forward prospects Reilly Smith and Matt Fraser, and defensive prospect Joe Morrow.
Stars General Manager Jim Nill said in a statement Seguin and Peverley will help Dallas "solidify a very important position, while allowing Jamie Benn to return to his natural spot at wing."
"Tyler is a dynamic player that will be a part of our core group for a long time to come," Nil said. "A player at his age, position and talent level are extremely difficult to acquire and we're thrilled to bring him into our organization."
Seguin had 16 goals and 16 assists in 48 regular-season games for the Bruins, but only managed one goal and seven assists in 22 post-season games.
Boston lost to Chicago in the Stanley Cup Finals.
Eriksson -- who had spent his entire career with the Stars -- had 12 goals and 29 points in 48 games for Dallas last season. He has 150 goals and 357 points in 501 games with the Stars.