The deal is for $5 million, a source confirmed to ESPN.
Neal, 25, has spent all five of his seasons with the Atlanta Falcons, where he played for new Cowboys defensive coordinator Dan Quinn after being selected 17th overall in the 2016 draft.
Although Neal has played safety in the first five years of his career, there is a possibility the Cowboys could use him as a weakside linebacker, which would have a domino effect on linebackers Jaylon Smith and Leighton Vander Esch.
If Neal sticks at safety with the Cowboys, he should be penciled in as a starter opposite Donovan Wilson. Xavier Woods, who started all 44 games he played from 2018-20, is also an unrestricted free agent.
Sources told ESPN that the Cowboys are scheduled to have visits this week with free-agent safeties Damontae Kazee, who also played for Quinn in Atlanta, and Malik Hooker. Both players had their 2020 seasons cut short by Achilles tears.
After injuries cut short his 2018 and '19 seasons, Neal played in 15 games for the Falcons last season, making 14 starts and finishing with 100 tackles, an interception and a sack.
Last season was his third season of 100 or more tackles. He had 106 in his rookie season and a career-best 116 in 2017, when he was selected to his only Pro Bowl.
His 2018 season ended after one game when he tore his ACL in the Falcons' season-opening loss to the Philadelphia Eagles. His 2019 season was over after three games when he tore his Achilles in Atlanta's Week 3 loss to the Indianapolis Colts.
Neal's salary with the Cowboys was first reported by NFL Network.
ESPN's Todd Archer contributed to this report.