Adrian Wojnarowski of ESPN reported earlier Friday that Horst signed for three additional seasons.
Gery Woelfel, a former Bucks beat writer for the Journal Times, reported on his own website that Horst was looking for a raise with one season left on a three-year deal signed in 2017.
Milwaukee finished a league-best 60-22 and made the Eastern Conference Finals this season.
Horst, whom Wojnarowski called an Executive of the Year candidate, hired ex-Atlanta Hawks head coach Mike Budenholzer to lead Milwaukee in 2017.
Budenholzer has led the team to a 104-60 record in two seasons, and its 60-22 mark last year was the team's best record since the 1980-81 campaign. The Bucks also made the Eastern Conference Finals for the first time in 18 years.
Horst also made a few key player transactions that helped lead to the Bucks' 60-win campaign.
First, he traded for Phoenix Suns guard Eric Bledsoe in 2017.
The nine-year veteran, who averaged 15.5 points, 5.5 assists and 1.5 steals last season, ranked ninth among qualified point guards in defensive real plus-minus, per ESPN.com.
Second, Horst signed center Brook Lopez to a one-year deal this past offseason. Lopez was a perfect complement to the remaining Bucks starters, as his ability to space the floor with his three-point shooting (36.5 percent) helped Milwaukee finish first in points per game.
Horst, 36, has been with Milwaukee since 2008 when he joined the team as its Director of Basketball Operations.