The 22-year-old Ward won the Kevin Sheedy Medal for his terrific season, in which he averaged 24 disposals in his 20 matches.
"Callan has consistently been one of our best players all year," coach Kevin Sheedy said.
"He is a tough hard midfielder who has shown strong leadership on and off the field to this young team. He plays with tremendous spirit and has a very big future ahead of him."
The experienced coach also heaped praise on Greene and Cameron for their terrific debut seasons at AFL level.
"For two first-year players to finish in the top three of the club's best-and-fairest is an incredible effort," he said.
"Toby's ability to find the ball and take on the contest has been a real highlight while Jeremy has had one of the best debut seasons of any young forward I've seen in more than 40 years in the game."
Greene - who was taken at pick 11 in the 2011 AFL Draft - averaged a superb 28.4 disposals per game, winning more than 30 in eight of his last nine matches.
Cameron kicked 29 goals in his 16 matches and finished second in Wednesday's AFL Rising Star count.
Former Melbourne midfielder Tom Scully finished fourth in the count, while ruckman Jonathan Giles was fifth.
Phil Davis, Chad Cornes, Luke Power, Adam Treloar and Devon Smith rounded out the top 10.Greene also claimed the Giants' rising star award, while Jacob Townsend won the coaches award.