The Shattenkirk deal is worth $17 million over four years for a $4.25 million average per year, a source told ESPN.com's Pierre LeBrun.
The 24-year-old Shattenkirk had five goals and 18 assists in 48 games last season. In four NHL seasons with Colorado and St. Louis, the former Boston University player has 23 goals and 86 assists in 201 games.
The 25-year-old Berglund, from Sweden, had 17 goals and eight assists in 48 games last season. In five seasons with the Blues, he has 92 goals and 96 assists in 358 games.
Information from The Associated Press was used in this report.