The long-rumored deal took several weeks to consummate after Orioles owner Peter Angelos hesitated.
The 28-year-old Bedard had the best season of his five-year career in 2007 with a record of 13-5, an earned run average of 3.16 in 28 starts (182 innings), just 57 walks and a franchise-record 221 strikeouts.
He was sidelined by an abdominal strain the final month of the season. His acquisition bolsters a Seattle staff that also includes ace right-hander Felix Hernandez.
"Erik adds a top-of-the-rotation starter to our club, and also makes our bullpen a lot stronger," said Manager John McLaren.
Jones, 23, long regarded as the Mariners' most prized prospect, spent much of last season at Triple-A Tacoma with 25 home runs and 85 RBI.