The former Manchester United forward swapped Old Trafford for the Emirates Stadium ahead of this season and has been receiving more time on the pitch as a result.
Hodgson was full of praise for Welbeck in the press recently and confessed that his perception of the striker could have played a part in his move to North London.
"I speak to him (Wenger) very often," Hodgson is quoted as saying by The Telegraph.
"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 [England] like Danny very much. We've always shown faith in Danny.”
Welbeck recently scored the decisive goal for the Gunners in their FA Cup victory over former club United in his first return to Old Trafford since leaving the Manchester club - where Arsenal won 2-1 on enemy soil.
The England international has been named in Hodgson’s most recent national squad for upcoming games against Lithuania and Italy.
Welbeck has scored four goals in 22 Premier League appearances for his new employers.
Despite wanting to play as a central striker, the form of Olivier Giroud has meant that the 24-year-old has most frequently been used on a wing by Wenger.