The Belgium midfielder arrived in 2013 from Everton but struggled under David Moyes.
However, Fellaini persevered at United, where Giggs coached him during his spell alongside Van Gaal.
And in Jose Mourinho’s set-up now, the 29-year-old has seen his strengths utilised to great reward.
His relationship with fans has improved greatly, with United now looking to tie him down on a new contract.
Reports suggest there are fears of losing Fellaini, with his current deal expiring next summer, unless he is handed a big pay rise.
But Giggs feels he has earned Jose Mourinho’s trust and is the perfect trainer.
"Marouane Fellaini has really proved his importance, stepping in for Paul Pogba," Giggs told Sky Sports.
"He has scored important goals, as he did at Everton and I’m really pleased for him after taking a lot of stick over the years.
"I've worked with him and he's a great lad to train because he does exactly what you want.
“He hasn't let the fans bother him because he's always had the support of the players and the coaches.
"He is effective, knows his strengths and limitations, and he's somebody who Jose has put a lot of faith in and he has repaid that with some important goals."
In the absence of injured Pogba, Fellaini could start for Manchester United in their crunch visit to Liverpool after the international break.
He already has four goals for the Red Devils this season across all competitions.
