The 36-year-old – making his third Olympic appearance – kicked off his Olympic campaign at Lord's Cricket Ground and shot a 72-arrow score of 680, firing himself into a strong position.
Bristol-born Godfrey was delighted to have started so well, despite falling short of a new British record.
"I’m very happy,” said Godfrey.
“It's a personal best. The British record was on, it was in sight. I let it go towards the end but I am happy.
"I thought I would be a bit lower than fourth. I've qualified before and I've shot similar scores and finished much lower.
"Last time in Antalya I shot a similar number and qualified 12th so I'm pleased."
Team GB finished eighth overall in the ranking event, meaning they missed out on a bye to the quarter-finals.
But Alan Wills, who finished in 42nd place with a score of 660, believes that he and Godfrey – joined by Simon Terry, who finished in 50th place – should be happy with their placing, which means they will face Ukraine.
Wills said: "We would have taken that number in the team ranking yesterday. We're all shooting good and in good form.
“I had a few jitters early on with a few silly errors in there but we are feeling confident."
Terry, a two-time medallist in Barcelona 20 years ago, was in philosophical mood after his ranking round, believing that he was up not up to scratch on the day.
He also pointed to the fine form of Im Dong-Hyun, who is technically blind, and Bubmin Kim, who both set new world records and are potential quarter-final opponents for Team GB.
He said: "I can't complain, I didn't make too many mistakes, the arrows just weren't going into the 10. I had so many nines.
"With two Koreans shooting world records and nearly always hitting 10, if you shoot an end of 54 you just lose ground without making mistakes. That's the sport though."