The deal is worth up to $2.5 million, including incentives, a league source said Thursday.
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Graham, who kicked for the Cincinnati Bengals last season, comes into Baltimore's camp as the challenger to veteran Billy Cundiff.
Graham struggled last season, missing 28- and 35-yard field-goal attempts in the Bengals' wild-card playoff loss to the New York Jets. But the 32-year-old Graham, who has 10 years of kicking experience, is also the fourth most-accurate kicker in NFL history.
Cincinnati is trying to replace Graham with NFL veterans Dave Rayner and Mike Nugent.
Sources: Baltimore Ravens close to deal with placekicker Shayne GrahamValencia confirm Emery deal