Jackson played the past five seasons in Minnesota, which chose him in the second round of the draft.
Terms of the deal are not known, and he can't sign a contract until Friday, which is the first day transactions may be filed with the league.
Jackson, 28, played in Minnesota under Darrell Bevell, who was hired to be Seattle's new offensive coordinator.
Jackson's role will be a question. Most likely, he will compete with Charlie Whitehurst for the starting job.
Hasselbeck's chance to re-sign with Seattle evaporated with the Seahawks' decision to acquire Jackson.
In Minnesota, Jackson started 20 games. The Vikings were 10-10 in those games, but he was supplanted by Brett Favre on the depth chart the previous two years