The unrestricted free agent has accepted a two-year offer to join the Cats, with an official announcement expected to be made at 3pm on Thursday.
His departure will mean Melbourne will receive a compensation pick at the end of the Gillette AFL Free Agency Period, having also lost Brent Moloney to the Brisbane Lions last Friday.
Melbourne picked up the Cats' Shannon Byrnes in the first week of free agency but the net effect will be a compensation pick to the Demons.
The AFL will allocate picks soon after the end of the free agency period at 5pm on Friday.
The selection allocated for Rivers will be vital in determining how active Melbourne is during the final week of the Gillette AFL Trade Period.
Trade tracker
The defender turned 28 on Thursday and has played 150 games for the club, including three finals. He has not played in a final since 2006.
In 2012, Rivers was outstanding in a tough year for the Demons, finishing fifth in the best and fairest, following a runner-up finish in the club award in 2011.
The defender played every game in 2012 and was outstanding in the back half in the first 10 rounds. He was close to leading the club best and fairest at that point, before being moved forward in round 11.
The season-ending injury to Mitch Clark meant Melbourne had little choice but to continue playing Rivers in his uncustomary role. He kicked 13 goals and was a stoic performer against the odds.
Despite losing his position in the leadership group at Melbourne, he is known to have adjusted well to the new-look football department and showed great leadership on and off the field during 2012.
Trade Machine
His decision to join Geelong came down to an opportunity for on-field success arriving sooner rather than later.
Melbourne offered Rivers a contract to continue but he deferred re-signing until he had the opportunity to explore his options. Collingwood expressed interest at one stage but Geelong emerged as the main suitor for his services.
The Cats have been keen to find a replacement in defence for retiring champion Matthew Scarlett and have been active in trying to fill some holes.
Rivers is a good judge of a mark, is well suited to filling the role of a third tall and shapes as a good fit.
He will not cost the Cats a draft pick as he is an unrestricted free agent.
