The Hawks swapped NAB AFL Draft pick 66 for the defender and pick 72.
Spangher joins Brian Lake in adding to the beaten grand finalists' key defensive options.
Since the end of the season, the Hawks have lost Thomas Murphy to Gold Coast, delisted back-up big man Jarrad Boumann, while Stephen Gilham's future is still unknown.
Trade tracker
Hawthorn will be Spangher's third AFL club.
The 25-year-old crossed to the Swans from West Coast at the end of 2010, after playing 26 games in five years at the Eagles.
He managed six senior games for the Swans in 2011, and none this year.
At 193cm and 90kg, Spangher will give Hawthorn coach Alastair Clarkson an extra option in covering opponents' key forwards.
He was also used as a forward by the Swans.
"For a long time we've admired Matt as a quality person, and we're confident he will fit in well with the culture of our club," Clarkson said.
Lake crossed to the Hawks from the Western Bulldogs on the opening day of the Gillette Trade Period.
More to come.
