The Giants announced on Monday that Scully, 20, had agreed to a six-year deal with the club, who enter the AFL in 2012.
The midfielder was taken with the first pick in the 2009 national draft by Melbourne.
GWS chief executive Dale Holmes said he met Scully and his family for the first time on Sunday, with the official contract signed on Monday morning.
"I got a great sense of how agonising it has been for Tom this year," said Holmes.
" ... we're delighted to have Tom at our club."
Scully informed Melbourne interim coach Todd Viney, football director Garry Lyon and several Demons players of his decision to swap clubs on Monday morning.
Melbourne vice-president Don McLardy and CEO Cameron Schwab will announce the club's response at a media conference at 1400 (AEST).
The Giants had tabled a huge offer for Scully - far more than the Demons could afford - and Scully admitted that was a significant factor.
"I also saw an opportunity be part of a brand new football club with access to so much young talent," said Scully, who said the move north would take him out of his "comfort zone".
The timing of the announcement was unlikely to have pleased cross-town rivals Sydney, who had scheduled Adam Goodes to speak ahead of his 300th game on Monday morning.
The Giants have signed fellow uncontracted players Callan Ward (Western Bulldogs), Phil Davis (Adelaide) and Rhys Palmer (Fremantle) - but Scully's signature is the biggest boon.
The 2009 No.1 draft pick has been linked to the Giants throughout the 2011 season.
The Demons' hopes of keeping Scully slowly but surely shrivelled from March 3 when he first spoke to the media about the speculation.
Melbourne endured a tough season, axing coach Dean Bailey after an embarrassing 186-point loss to Geelong in July.
Viney is caretaker coach with no long-term replacement announced.
Scully has played 31 games in total but battled a knee injury this season that restricted him to 10 games.
The Giants are likely to make him a co-captain.
