The agreements are pending physicals, Schefter adds.
However, the team is expected to kick off the 2020 season without second-year wideout Deebo Samuel, who suffered a foot injury this offseason. General manager John Lynch previously said Samuel "may miss some games."
Austin, 30, appeared in 14 contests for the Cowboys in 2019, amassing just 13 receptions for 177 yards and one touchdown. The 2013 eighth overall pick, who can also contribute as a punt returner, enjoyed a career year with 58 catches for 509 yards and three scores with the Los Angeles Rams in 2016.
Nelson, meanwhile, played in just two games with the Raiders last season. The 28-year-old's best campaign came with the Arizona Cardinals in 2016, when he racked up 34 catches for 568 yards and six touchdowns.