The Giants sent talented zone-listed Northern Territory youngster Jed Anderson, along with picks 29 and 68 to the Hawks, in exchange for Gilham, pick 28 and pick 65.
Gilham was an important member of Hawthorn's 2008 premiership team, but couldn't cement a place this season after rupturing his anterior cruciate ligament in 2011.
The 28-year-old's manager Dan Richardson said his client's move would open up more senior opportunities and help set him up for a future coaching career.
"It was always a bit of a question mark as to what his situation at the Hawks would be; Brian Lake coming in made it potentially a bit more difficult for him," Richardson told AFL.com.au's Trade Radio on Friday.
"There's never any guarantees in footy but it gives him an opportunity to play plenty of senior footy this year whereas that was 50-50 at the Hawks."
Richardson said Gilham would be a perfect fit with a young Giants' backline that included Phil Davis and Tom Mohr.
Anderson is an 18-year-old, 181cm midfielder and half-back who attacks the ball hard and can run and carry.
He has played the past two seasons for the NT Thunder, after moving home from Sydney, where he had gone to join the Giants' scholarship program as a 16-year-old.
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Gilham played 98 games for the Hawks after crossing from Port Adelaide at the end of 2005.
He had managed only one senior match for the Power.
