Welbeck joined Arsenal in September last year after a frustrating spell at Manchester United, where he often played out wide.
Hodgson revealed he regularly spoke to Wenger, with the Frenchman consulting the 67-year-old manager before signing Welbeck.
"I speak to him [Wenger] very often," Hodgson said of Wenger.
"We spoke of course before he signed him [Welbeck] and I was singing Danny's praises, so I'm delighted Arsene has seen that my judgment wasn't wrong and that he shares that judgment.
"We like Danny very much [with the national team]. We've always shown faith in Danny."
Hodgson has been happy with the amount of game time Welbeck has received at Arsenal, but he would love to see the 24-year-old playing even more.
"He's played quite a lot of games for Arsenal if you compare it to the number of games he was playing at Man United," he said.
"With us, he's always done what I think is a very, very good job for the team. There's not many times he's played for England when I've been disappointed in him."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.