The 27-year-old spent most of last season with Triple-A Tacoma, where he batted .247 with nine doubles, 15 home runs and 45 RBIs in 78 games.
Nelson started the 2009 season with the Brewers and had just 21 at-bats before being sent to the Minors. Nelson refused the assignment and signed with Seattle as a free agent on May 21.
A fourth-round selection by the Brewers in the 2001 First-Year Player Draft, Nelson played 28 games in the big leagues, going 2-for-28, in parts of the 2008 and '09 seasons.
In the Minors, he has batted .268 with 227 doubles, 116 home runs and 569 RBIs in 3,479 at-bats.
Nelson figures to compete with Mike Carp as a backup to Casey Kotchman at first base, and for a spare outfield spot during Spring Training, which begins on Feb. 18 at the Peoria Sports Complex.
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.