The deal can max out at $3 million, the source said.
He is the second defensive player to return in as many days, joining defensive end Dorance Armstrong, who signed a two-year deal worth a max of $13 million.
The Cowboys had conversations with veteran Bobby Wagner to reunite with Quinn, but they had not gone far. The Cowboys have mostly focused on re-signing their own free agents so far and have had talks with safety Jayron Kearse, who led the defense in tackles.
After the Cowboys decided against his 2022 fifth-year option because of injury concerns, Vander Esch made 16 starts while playing in every game last season.
He finished third on the defense with 77 tackles, and he also had a sack, 3 tackles for loss, 5 quarterback pressures, an interception and 2 passes defended.
After he was selected with the 19th overall pick, Vander Esch exploded onto the scene while starting 11 of 16 games in 2018, becoming the first Cowboys linebacker to be named to the Pro Bowl as a rookie. He finished with a franchise rookie record for tackles in a season (credited with 176 by coaches) and a single game (19 vs. the Philadelphia Eagles).
Vander Esch, who turned 26 in February, missed seven of the final nine games in 2019 with a neck injury that ultimately led to surgery. He started all 10 games in which he appeared in 2020, suffering a broken collarbone in the opener and a high ankle sprain with two games to go.
The Cowboys released starting right tackle La'el Collins on Thursday, saving $10 million against the cap. The team also lost defensive end Randy Gregory to the Denver Broncos in free agency earlier this week.