Tyson, 20, was selected by the Giants with pick No.3 in the 2011 draft and played 13 games for the club, after being restricted to three matches this year due to a knee injury.
He was packaged up with draft picks nine and 53 by the Giants, who will be recompensed with selections two, 20 and 72 from the Demons.
GWS already held first pick in next month's draft after claiming the wooden spoon in 2013.
"Dom is a tall midfielder who is exceptional around the stoppages and has a unique ability to find a gap in traffic," said Melbourne's football operations manager Josh Mahoney.
"He is strong overhead, he has good touch and depth with his kicking.
"Dom comes with a good strong character, and fits the age and positional profile that we need to improve upon. He complements our young core of midfielders who can grow together over the next 10 years.
"Dom also has the benefit of being in the AFL system for two years as he understands the level of competition and the standards required to be a professional AFL player. He can come in and play straight away."
The arrival of Tyson adds to the recruitment already of Melbourne of 21-year-old midfielder Viv Michie from Fremantle.
Despite playing just the one AFL game in three years largely because of foot injury issues, Michie also looks capable of adding to Melbourne's midfield in 2014 coming off a season that saw him win his WAFL club Peel Thunder's fairest and best award.