Wilshere has revealed that Welbeck broke the news of the transfer to him during an England training session.
"I remember speaking to Danny in the England camp on deadline day and he said it was on," Wilshere told the Daily Mirror.
"I thought he was joking. I was reading that Tottenham were interested and then he said that Arsenal were interested.
"As soon as he said we were interested I was telling him 'you've got to come'. He gives us something different, he runs behind. Because we lost Olivier Giroud, we needed a key man."
Welbeck has scored four goals in six appearances for the Gunners so far.