Boston also acquired forwards Matt Fraser, Reilly Smith and defenceman Joe Morrow.
Dallas also received forward Rich Peverley and defenceman Ryan Button.
Seguin was drafted second overall by Boston in 2010 and won the team's scoring title in the 2011-12 season.
The winger was a member of the Bruins 2011 Stanley Cup championship team and was selected to the NHL all-star game in 2012.
Eriksson had 29 points in 48 games for the Stars last season. He has a career plus-31 rating and played in the 2011 all-star game.