The 22nd-overall pick in 2015 signed a one-year deal with the Knicks in July 2019 that included a club option, which was declined by the team earlier this week.
Portis, 25, averaged 10.1 points and 5.1 rebounds per game for the Knicks last season, his fifth in the National Basketball Association.
The addition of Portis to Milwaukee's frontcourt will fill some of the vacancies created by the departures of Robin Lopez and Ersan Ilyasova.
In the 2018-19 season, the 27-year-old shooting guard appeared in all 82 games, starting 81, and averaged 11.8 points, 2.9 rebounds and 2.1 assists.
Augustin, 33, will be joining his ninth team in 13 National Basketball Association seasons.