The Manchester United manager said Welbeck was not up to the required standard of a United striker, and that was why he was allowed to join the Gunners.
"He doesn't have the record of RVP or Rooney, that's the standard," van Gaal told reporters ahead of United's game against Queens Park Rangers this weekend. "That's why we let him go."
Falcao & Blind press conference
Van Gaal was speaking at the press unveiling of Radamel Falcao and Danny Blind, two of his late additions before the close of the summer window.
Van Gaal went on to praise Falcao as 'one of the best strikers in the world', hailing his 'unbelievable' record in front of goal.
That was the chief criticism of Welbeck at United, as his goal record was not the best. In his defence he was often played on the left flank and couldn't break past Rooney or Robin van Persie to stake his claim for a regular place as central striker.
At Arsenal he'll get that opportunity from the go, as first-choice forward Olivier Giroud is sidelined until December at the earliest after suffering injury against Everton.
He showed what he can do through the middle for England in mid-week, scoring both goals as England beat Switzerland to open their European Championship qualifying campaign with three points.
United fans were largely split 50-50 on Welbeck's departure. It's hard to argue that he stood to play a significant amount of time as a striker following the capture of Falcao, adding to Rooney and van Persie.
Man United transfer news
But at the same time many former-Manchester United players have questioned the decision to sell the 23-year-old, who came through the club's academy system.
Welbeck had been at the club since age nine, and many felt his sale represented the end of a tradition of handing youth a chance at Old Trafford.