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."
