Sky Sports News revealed on Sunday that the 28-year-old had completed a Rangers medical ahead of his move from the Serie A side.
Godfrey becomes Rangers' third summer signing after the arrivals of Lawrence Shankland and Ross McCrorie.
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The Englishman moved to Atalanta from Everton in the summer of 2024, but has since been on loan at Ipswich, Sheffield United and Brondby.
On signing for Rangers, Godfrey said: "I am buzzing, I am really happy to be here. I know the size of the club, so it is a massive honour to be wearing the shirt this season, and I can't wait to get started.
"I am looking forward to meeting the boys and hopefully helping this club achieve what it deserves, which is silverware and exciting times."
Gers boss Derek McInnes said: "Ben is a player who has competed at a very high level throughout his career. He's played in the Premier League, been involved with England, and brings a lot of experience with him.
"He's a strong, athletic defender with good qualities both on and off the ball, and we believe he can add a lot to the squad. We're pleased to get him in, and I'm looking forward to working with him in the season ahead."
