If the Hawks choose to use the pick in this year's draft, they must notify the AFL by November 5.
The compensation offered to the Hawks was the same as Adelaide received for losing Nathan Bock and the Brisbane Lions received for losing Michael Rischitelli.
Earlier on Wednesday, Brown said rumours that Hawthorn offered him up for trade at the end of 2009 had no bearing on his decision to leave the club.
Brown, 27, was officially revealed as the Suns' fourth uncontracted player-signing on Wednesday, joining Bock, Port Adelaide's Nathan Krakouer and Rischitelli at the fledgling club.
Rischitelli, the Lions' reigning club champion, joined Gold Coast after he was offered to Carlton in a proposed trade for Brendan Fevola at the end of 2009.
It was widely reported that Brown went through a similar ordeal as the Hawks offered him to Port Adelaide as part of an exchange for midfielder Shaun Burgoyne.
However, Brown said ohe incident, which was denied by the Hawks at the time, did not influence his choice to move north.
"There were those rumours circulating that my name got thrown up but I can categorically say that had no impact on my decision," he said.
"Those are the type of things that happen in AFL footy these days and we worked that out at the end of last year and that had no bearing at all on my decision.
"There have been reports that there have been hard feelings; that I was hurt and that kind of thing, but that's not correct at all."
Instead, Brown said the prospect of becoming a leader among a young group and reclaiming a place as a permanent defender swayed him to join the Suns.
"Just over the last couple of years, through no fault of my own or the coaching staff, I've had to play forward and back and a lot of different roles," he said.
"While it's always good to be flexible and I like being a flexible player, it's often quite difficult as well to be chopping and changing a lot mid-game and mid-season.
"I love playing down back and that's where I want to see my role in the side."
Brown said he left the Hawks with no hard feelings among the coaches or the players, and maintained the club's premiership window remained open despite its failure to get close to matching its 2008 success.
The Hawks' rapid rise from 15th in 2004 to premiers four years later was a model the Suns could emulate, he added.
"When Alastair Clarkson became coach in 2005, we had a pretty similar club. We were very young and very exciting," he said.
"Guys like Franklin and Lewis and Roughead hadn't played any footy at all, and it only takes one, two, three years for those guys to grow and develop.
"You can turn young sides into pretty competitive sides very quickly in today's football, especially with the coaches the Gold Coast have."
Suns coach Guy McKenna said Brown's character and playing style would complement the club's values and the relative inexperience of its squad.
"Dean Solomon, our defensive coach, [is] going to coach similar traits into the boys and to have a player of Campbell's ilk, a premiership player, to actually go out and follow those instructions … he'll be a great fit for our football club," he said.
