Bennett signed a contract on Thursday and Foye accepted a one-year deal. While the team did not divulge the terms of Bennett's contract, multiple reports had it as a two-year pact worth the veteran's minimum.
Brooklyn also signed guard/forward Caris LeVert to a multi-year contract.
Bennett was selected with the first overall pick in the 2013 draft but struggled mightily in three seasons with Cleveland, Minnesota and Toronto. The 23-year-old Canadian averaged just 4.2 points and 3.1 rebounds during those stints.
"We have been excited to watch Anthony's progress this summer with his national team, and look forward to the opportunity of having (coach Kenny Atkinson) and his staff work with him to continue his development," Nets general manager Sean Marks said.
A 6-foot-8 power forward, Bennett was traded along with Andrew Wiggins from Cleveland for Kevin Love in 2014 following a disastrous rookie season.
Foye played in 81 games last season with Denver and Oklahoma City. The 32-year-old averaged 6.0 points and 2.1 assists in 54 contests with the Nuggets and 5.6 points in 27 tilts with the Thunder.
LeVert averaged 10.4 points, 3.5 rebounds and 2.7 assists in 103 career games with Michigan.