The 20-year-old, who was traded to the Demons by Greater Western Sydney last Friday, struggled with injuries during his two seasons at the Giants, playing only 13 games for the club.
Tyson was grounded for the first half of this year by a serious knee problem, and his only AFL appearances came in the last two rounds.
But he says he has arrived at Melbourne in good shape.
"We just had a couple of little meetings there with (elite performance manager) Dave Misson and the physios, but I think I'll be rolling into pretty much full training," he said at the Demons' AAMI Park training base on Tuesday.
"There might be a little bit of modified stuff, but hopefully early days I'll be in full training.
"I missed a chunk of training last year, so touch wood, this will be my first full pre-season."
The No. 3 pick in the 2011 NAB AFL Draft, Tyson grew up in Melbourne and was reportedly homesick during his time in Sydney.
However, he says he was not actively trying to leave the Giants.
"I was contracted, so I hadn't really had too much of a thought about it," he said.
"But when my management said there could be a pretty serious chance to get back, that's when I thought it would be great to return to Melbourne and be around family and friends again.
"I enjoyed it up there - they're an exciting club at the Giants, and I've got some close mates up there.
"So I guess it was a tough decision. But I'm very excited with this."
Tyson was in Hawaii when he was informed that Melbourne had made a play for him.
"I was over there for Setanta O'hAilpin's wedding and got called back by my management to have a meeting," he recalled.
Upon his return, Tyson was taken to the home of Melbourne's head of player development, Todd Viney, where he met the club's new coach Paul Roos, new assistant coach George Stone and football manager Josh Mahoney.
"I was impressed by the presentation from the Dees," he said.
"It was very exciting. (Roos) was very honest, and that was something I really appreciated.
"He said, 'We need to add some midfield depth. I've followed you for a couple of years, and we're excited by the proposition of putting you through the midfield.'"
A day later, the deal was done.
Melbourne gave up picks 2, 20 and 72 in the upcoming draft, with the Giants handing over Tyson, picks 9 and 53 in return.
