The person spoke to The Associated Press on condition of anonymity Sunday night because the team has not announced the deals.
The team is set to pay Butler $4.5 million next season, with an option for 2015-16. Augustin will make $6 million over two years.
Detroit has missed the playoffs the last five seasons, and the Pistons recently hired Stan Van Gundy as their new coach and team president. The first order of business this offseason has been to add some perimeter help for the team's imposing set of big men.
The 6-foot-7 Butler played 56 games last season for Milwaukee and Oklahoma City, averaging 10.5 points and shooting 39 percent from 3-point range.
Augustin was waived by Toronto early last season, but the 26-year-old point guard caught on with Chicago after that and ended up averaging 13.1 points for the season. He shot 40 percent from beyond the arc.
Only one Detroit player in 2013-14 - Kyle Singler - shot over 34 percent from 3-point range while playing major minutes. The Pistons were unable to take advantage of big men Andre Drummond, Greg Monroe and Josh Smith because of the team's inability to produce outside the paint.
Monroe is a restricted free agent, but if he comes back, Detroit would still have an imposing frontcourt. The Pistons now have more options on the perimeter as well, with Meeks, Butler and Augustin joining holdovers Singler, Brandon Jennings, Will Bynum and Kentavious Caldwell-Pope.
AP Sports Writer Larry Lage contributed to this report.