Vidic left United this summer having amassed 15 trophies during his eight years at the club.
His final season at Old Trafford proved to be a trophyless and joyless experience for the Serb, though.
Under David Moyes' stewardship, United ended the campaign in seventh position - their worst finish in the Premier League era.
But with former Barcelona and Bayern Munich manager Van Gaal now at the helm, Vidic thinks things are looking up for United.
"Van Gaal has a lot of experience, he has trained a lot of teams in a lot of leagues and that shows he knows what he is doing," the new Inter Milan centre-back said after playing United in a friendly on Tuesday night.
"I believe he can do good work and the players think the same.
"I was in the dressing room with the players after the game and they were all positive and happy with everything that is happening at the moment.
"That is a good sign
I am pleased to see that.
"They are happy with what they are doing and for that reason it will not be difficult for them this year."
Moyes maintained it was a "mutual" decision for United and Vidic to part ways this summer, even though many fans were happy for the 32-year-old to stay.
Despite his praise for Van Gaal, who has a far more illustrious CV than Moyes, Vidic does not think leaving United for Inter was the wrong move.
"I don't have regrets," said Vidic after the game, which United won 5-3 on penalties after a 0-0 stalemate over 90 minutes.
"That's (in the) past
What I must do now is look to the future, the same as Manchester United have to do
I am a fan of Manchester United and I hope both teams do well this year."
Vidic's departure, and that of fellow experienced defender Rio Ferdinand, has left a huge gap in the United team.
There is a feeling within the club that despite their previous troubles, Chris Smalling, Phil Jones and Jonny Evans are primed to have the best year of their careers to date.
There is a lot of responsibility on the trio given that Van Gaal looks set to play 3-5-2 this year.
The Dutchman, who has also used academy graduates Tyler Blackett and Michael Keane on the tour of the US, is in the market for at least one centre-half, with Thomas Vermaelen and Mats Hummels top of his list.
But Vidic thinks Evans, Smalling and Jones are good enough to make the step-up and become first-team regulars this year.
"Of course I think they are good enough to do it," the former United skipper said when asked about the trio.
"I was sure of that even when I played with them
I said then they have really good potential, physically and technically.
"They are really good and they are young.
"They are getting better and better every year.
"In the next two years they will be I think some of the best defenders in the league
I think they will prove that this season and I wish them all the best."
Source : PA
Source: PA