"How can you say 'no' to Melbourne Victory," said the goalkeeper, whose contract with disgraced Perth Glory was terminated by both parties at the end of the season after the club was found guilty of salary-cap breaches and kicked out of the finals.
He signed a three-year contract with Victory in June.
"Victory are a huge club, the biggest I will have ever played for," Vukovic said.
"Once I mutually terminated my contract with Perth, Victory showed interest. And once they showed interest there was only one place I wanted to go.
"Victory is coming off a very successful campaign and I hope to make them even stronger. I definitely feel a responsibility because I have to prove myself again."
He added: "But there are other reasons for joining Victory. The lure of Champions League football was a factor too but not only that. The professionalism of the club, the supporters and the fact they are a champion side made my mind up."
Vukovic admitted that his family was also a decisive factor in making the move.
"My wife Kristy and I are about to have our first child so I wanted to be closer to home," he said.
Sydney-born Vukovic, 30, has yet to win an A-League championship after playing for beaten grand finalists Central Coast Mariners in 2006 and 2008 and Perth in 2012.
He admitted that helping Victory to successive championships after losing three grand finals was one of his priorities.
"Winning the title is one of my main targets, definitely," he said.
"But most importantly for me I want to play well and consistently for my new team.
"I would love to win the A-League in my first year at Melbourne Victory and help them go back to back."
Victory's game is heavily based on attack and coach Kevin Muscat is not expected to change his winning formula in season 11.
It was put to Vukovic that Victory's offensive style might leave its defence exposed to quick counter-attacks even though defensive midfielders Carl Valeri and Mark Milligan offer adequate protection.
The goalkeeper said he did not envisage any problems in this area in the coming season.
"I am not concerned at all, to be honest," he said.
"Victory were statistically the best defensive team in the league last season and I don't feel I will be exposed at all.
"I will need to make saves same as every keeper and I cannot wait to play in behind this team."
Victory starts its pre-season training on 13 July.
