The deal is worth $1.23 million, but Weeden is due a remaining $2.1 million from the Browns.
Weeden, 30, is a former Browns first-round draft pick from Oklahoma State who has passed for 5,116 yards with 23 touchdown passes and 26 interceptions.
Weeden is expected to back up Tony Romo.
Kyle Orton is expected to retire.
Orton has a $3.25 million base salary for next season.
If he retires, Orton would owe the Cowboys $3 million.
Orton received a $5 million signing bonus when he joined the Cowboys.
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Aaron Wilson covers the Ravens for The Baltimore Sun