The 29-year-old was traded from Port Adelaide as part of a three-way deal on the second-last day of the Gillette AFL Trade Period.
Port received Lewis Stevenson from the Eagles in the exchange, while the Demons sent pick 88 to West Coast.
"I'm extremely excited to get another opportunity," he told AFL.com.au from Adelaide.
"Melbourne Football Club has obviously shown a lot of faith, I just can't wait to start training and be a part of it."
Trade Period hub
Rodan visited Melbourne's AAMI Park facilities in recent days and was taken on a tour by captains Jack Grimes and Jack Trengove.
"I'm extremely impressed with what they've had to handle within the last year. From what I got from the day, the club's in very good hands."
Rodan adds bite to Melbourne's midfield and Demons coach Mark Neeld is also hopeful the veteran can offer great guidance to the club's rising stars.
"I think everyone knows they've got a pretty young list. Hopefully (I can) be someone they can go to and help them out and hopefully fast track them to the future."
He said Neeld has shown great faith in giving him a chance to start afresh at what will be his third AFL club.
"They've got some really good people there, I was super impressed with them. I just hope I can repay them and play some good footy."
Adding to the delight, Rodan's wife and young children will be able to move back to their home city to join their extended families.
While Port Adelaide had signalled its intention to cut the veteran midfielder, it hadn't formally delisted him allowing for what's essentially a trade of good faith to be completed.
The deal was clinched on Thursday afternoon when Rodan's manager Liam Pickering and Melbourne list manager Tim Harrington met to complete paperwork.
Rodan began his 176-game career at Richmond.
Matt Thompson is a reporter for AFL Media. Follow him on Twitter @MattThompsonAFL
