According to TFP Editor-in-Chief David Pagnotta, players involved in the trade started being notified of the deal around 2:15pm ET. Eriksson agreed to waive his no-trade clause earlier in the day.
The Bruins had been entertaining trade calls for Seguin for the last two weeks, with the Calgary Flames and Tampa Bay Lightning also interested.
In 48 games with the Bruins this past season, Seguin registered 16 goals and 16 assists for 32 points.
Peverley, 30, collected six goals and 12 assists for 18 points in 47 games with Boston.
Eriksson, 27, tallied 12 goals and 17 assists for 29 points in 48 games with the Stars this year.
TSN's Darren Dreger first broke the news that a trade between the two clubs was in the works.