The 23-year-old striker moved from Manchester United to Arsenal for a reported fee of £16 million in a last-minute deal on transfer deadline day.
Welbeck, a product of United's youth academy, made just 15 Premier League starts for the club last term.
And after United brought Radamel Falcao to the club, on loan from Monaco, he fell further down Louis van Gaal's attacking pecking order.
The England man subsequently moved to Arsenal and Hodgson feels regular football under Arsene Wenger will help Welbeck move to the next level.
"When you are a player of his calibre and find yourself at United with competition for places, you don't always get the starts you would like," Hodgson said ahead of England's friendly against Norway on Wednesday.
"He is going to a club where he will hopefully get more starts and playing time.
"It is not easy for players playing a small part in club games, then coming and playing 90 minutes for England in intense surroundings.
"So I am pleased for Danny and I think Arsenal have signed a good player."
Hodgson did not wish to offer any suggestions as to how Wenger should use Welbeck, but added that regular first-team exposure would help his cause as England boss.
"My job is with England and the players I choose," he added.
"I don't wish to make any suggestions about what clubs do with their players.
"But I cannot deny the more players play and the more experience they get, especially at Champions League level, the better it is for me at international level."
