Lee, selected in the second round with the 55th overall pick, was the last of the Cowboys' seven picks to agree to a contract. The Cowboys open training camp Saturday in San Antonio.
A source said the deal is for $3.5 million, with a $1.2 million signing bonus as part of $1.7 million in guaranteed money.
The Cowboys gave up their fourth-round pick to move up four spots in the second round to draft Lee. They ranked the former Penn State linebacker as the No. 16 player on their draft board.
The 6-foot-1, 236-pound Lee will compete with Jason Williams, the Cowboys' third-round pick last year, to fill the nickel linebacker role this season. Lee will back up veterans Keith Brooking and Bradie James, but coach Wade Phillips has said he expects the rookie to get significant playing time this season.