Welbeck, 23, has scored 10 goals in 20 appearances for club and country since being allowed to leave Old Trafford for £16 million ($25.1 million, 20 million euros) on transfer deadline day in September.
The Manchester-born forward will come up against his old team-mates for the first time when United visit the Emirates Stadium for the stand-out Premier League clash of the weekend.
Dutchman Van Gaal attributes Welbeck’s success at Arsenal to being a regular in their first team, after he was made to wait for opportunities during his time at United.
“I think that a player who is playing mostly fixed in the team, he develops and always will,” Van Gaal said.
“He takes all the benefit from playing every week. That was a question mark with Manchester United. It’s good to see he’s doing what I thought.”
Van Gaal accepted that Welbeck would enjoy scoring against his old club, much like United’s ex-Arsenal forward Robin van Persie has when he has found the net against the team he left in 2012.
“This is the football world,” Van Gaal said. “Van Persie has scored already three goals against Arsenal as a United player. That’s life, believe me.”
United will have goalkeeper David de Gea available at the Emirates, despite suffering a dislocated finger while on international duty with Spain.
Angel di Maria and Michael Carrick have also recovered from minor injuries, but left-back Luke Shaw is a doubt after being hurt during England’s 3-1 friendly win over Scotland.
Van Gaal last faced Arsene Wenger’s Arsenal in 1999, when he was manager of Barcelona.
– Giroud returns –
The teams drew 1-1 at Camp Nou before the Catalan club won 4-2 at Wembley Stadium –- Arsenal’s adopted home in Europe that season — in the Champions League group stage.
Van Gaal, 63, says he is aware of the rivalry between his current club and Arsenal.
“It’s the first time I’m sitting on the bench against Arsenal as United coach,” Van Gaal said. “I have faced them when I was with Barcelona, then Wenger was on the bench.
“The way they play for such a long time, he has an attacking way of playing, playing for the fans. The rivalry is normal in sport. It should be abnormal when it’s not like that.”
Wenger’s players, meanwhile, will want to show their manager that he was wrong to write off his team’s title hopes.
Arsenal signed off for the international break by losing 2-1 at Swansea City, prompting Wenger to declare that no club currently looks capable of overhauling leaders Chelsea.
It was the second time in a week that Arsenal had conceded a lead, after they let a 3-0 lead slip to draw 3-3 with Anderlecht in the Champions League, and it left them 12 points adrift of Chelsea in sixth place.
Olivier Giroud will return to the Arsenal squad for the first time since breaking his leg at Everton in August to provide competition for Welbeck up front.
Welbeck continued his run of scoring form for England with two goals in last Saturday’s 3-1 win against Slovenia, taking his tally to five goals in five games for his country.
But with Welbeck having netted only once in his last seven club appearances, Giroud’s unexpectedly early return could prove timely.
Mikel Arteta also returns to the squad after missing the trip to Swansea with a hamstring problem.
“Giroud and Arteta are both available,” said Wenger. “It’s just a question of how ready they are. But they are available.”