Per ESPN's Adrian Wojnarowski, Brogdon's contract is worth $85 million over four years.
Wojnarowski added the Pacers will send Milwaukee three future draft picks, including one first-rounder, to complete the deal for Brogdon.
Brogdon was a restricted free agent, but the Bucks opted not to re-sign their point guard after Wojnarowski reported Khris Middleton signed a five-year, $178 million deal with the team.
A second-round pick by the Bucks in 2016, Brogdon quickly established himself as a valuable piece of the team's rotation. He was named the 2016-17 NBA Rookie of the Year after averaging 10.2 points and 4.2 assists in 75 games.
The 26-year-old was even better in 2017-18 with 13.0 points and 3.3 rebounds per game. He took his game to another level under head coach Mike Budenholzer last season, averaging a career-high 15.6 points and 4.5 rebounds while shooting 50.5 percent from the field.
Brogdon led the NBA with a 92.8 free-throw percentage and became the first player since Stephen Curry in 2015-16 to join the 50-40-90 club last season. He missed the Bucks' first eight playoff games because of a torn plantar fascia in his right foot suffered in a March 15 game against the Miami Heat.
Letting a player like Brogdon leave seems strange for a Milwaukee team that led the NBA with 60 wins. There are, unfortunately, practical concerns for the franchise to consider.
Giannis Antetokounmpo is signed for two more seasons, but presumably the Bucks would like to work out an extension with their franchise player as soon as possible.
Brogdon was a terrific steal for Milwaukee in the 2016 draft and could take the skills he learned to the Pacers.
Indiana found a perfect player who fits what the team needed. Brogdon's ability to shoot gives the offense an element that was sorely lacking when Victor Oladipo's season ended in January with a ruptured quad tendon.
Brogdon also offers the Pacers some insurance at the start of the season with the club expecting Oladipo to be out until at least December.