Bellamy began life with his home-town club with a goal and two assists as Cardiff beat Doncaster 4-0 on Saturday.
"I think he feels accepted... I think he could stay at Cardiff for the rest of his career, I think that's how much he likes it there," Savage told 5 Live.
"He's a fantastic player, one of the hardest-working... I've ever seen."
Cardiff have already beaten Savage's Derby County side, winning 2-1 at Pride Park in the second round of Championship matches, but the return at the Cardiff City Stadium on 2 April should be an interesting encounter between the two Welshmen.
As well as the surprise capture of Wales captain Bellamy, midfielders Jason Koumas, Seyi Olofinjana and Danny Drinkwater have all arrived for the season on loan from Premier League teams.
Despite debts estimated at £30m, Cardiff now appear to have one of the strongest squads in the Championship and last season's beaten play-off finalists are now one of the favourites to finally make the leap to the Premier League.
Gary Speed, now manager of Cardiff's Championship rivals Sheffield United, believes Bellamy can step back up to the Premier League whenever he wants to - although the former Wales captain has a suspicion Bellamy may be able to do it with Cardiff.
"I thought Craig was Manchester City's best player last season, you take his goals into account but if you look at all his assists - especially when he was linking up with Carlos Tevez - everything that Man City did went through Craig Bellamy really," Speed told BBC Radio Wales' The Back Page.
"I'm a massive fan of the way he plays; Craig Bellamy can still play at a higher level, no doubt about that, I just think it's the circumstances he finds himself in are a bit unfortunate.
"But he'll be delighted to be playing for Cardiff, his home-town club which he's always expressed he wanted to do.
"I think he'll be the best player in the division by a country mile, that's no surprise to anybody.
"But... one thing he will find in the Championship is the honesty of the players - they all want to do well, they all want to try hard and everyone seems to give 100%, which I think he'll find refreshing.
"He's a creative player that not many clubs in the Championship have and the bookies are very rarely wrong and I think Cardiff's odds have been slashed and I think rightly so.
"If I was to put any money on anybody - which obviously I can't do because of Football League rules about betting! - then I would put it on Cardiff.
"Good luck to them and I'm very pleased for Dave Jones."
Source: BBC Sport