Moore's deal is worth a maximum of $32 million, including $18 million in the first three years, a league source told ESPN NFL Insider Adam Schefter.
A 2009 second-round pick, Moore was expected to command a salary near the top of the safety market. San Diego's Eric Weddle, whose deal last July averaged roughly $8 million, has the top salary for a safety.
Moore, an integral part of the Atlanta secondary, made the Pro Bowl as an alternate last season.
Moore, 27, finished fifth on the team with 75 tackles last season despite missing four games with a hamstring injury. He also added four interceptions in 2012, giving him 11 over his four-year career.
Also Saturday, right guard Garrett Reynolds, who started seven games last year before having season-ending back surgery, agreed to a two-year contract.
Information from The Associated Press was used in this report.