The Nets also sent a 2019 second-round draft pick to the 76ers. They waived Ware on Saturday.
Teague, 21, had 10 points, four assists and six turnovers in Brooklyn's preseason finale Wednesday night in Boston.
Teague will make $1.1 million in 2014-15 and has a $2 million team option for 2015-16.
The Nets have now pared their roster down to 15 players. Earlier Thursday, they waived big man Willie Reed.
Jerome Jordan and Cory Jefferson are the other players on the team's roster with unguaranteed contracts. Jordan has impressed during the preseason, and it looks like he has done enough to make the team.
NBA rosters must be set for opening day by Monday at 5 p.m. ET.