Magilton, 42, will take over from Mehmet Durakovic, who was relieved of his duties as head coach on Friday after seven months in charge.
The former Northern Ireland midfielder spent three seasons as Ipswich manager between 2006 and 2009, before seven months in charge of QPR between June and December 2009.
He most recently served as an assistant coach with Irish Premier League champions Shamrock Rovers and was closely linked with the Northern Ireland coaching job before the appointment of Michael O'Neill.
Magilton received a telephone call from the club on Thursday following Victory's midweek loss to Central Coast Mariners before he flew into Melbourne on Saturday morning.
"It all happened pretty quickly," Magilton admitted.
"I got a phone call, the opportunity arose and I snapped it up.
"I am sitting here because the season thus far has not been as productive as we would all have hoped, but that is not to say that the second half of the season can't be great."
Magilton missed out on the Victory job when Durakovic was appointed in the close-season, but the club was impressed with the way he handled himself during the interview process.
Magilton continued: "I am fearless, I am meticulous, I am astute, I am very much hands-on and I like to get amongst the players and be involved in the training aspect of the set-up. And I am a pretty amiable guy.
"But the immediate effect I can have on the team is confidence, morale in the dressing room and to lift the confidence and morale of the supporters.
"That is something that I am easily equipped to do as it is in my nature."
Kevin Muscat guided Victory in Saturday's home win against Newcastle Jets at AAMI Park. He will now act as Magilton's assistant for the remainder of the season.