Axford received a $5 million deal, plus incentives. According to a baseball source, Badenhop signed for $1.55 million, while Estrada agreed to a $1.955 million deal.
With those three signings, plus that of outfielder Carlos Gomez on Thursday, Milwaukee avoided going through arbitration with all four of its eligible players.
Axford, 29, was arbitration-eligible for the first time after earning $525,000 last season, during which he briefly lost his closer's job but still saved 35 games and compiled a 4.67 ERA.
Badenhop, 29, was acquired from the Rays in early December and was up for arbitration for the third time. He earned $1.075 million in 2012 while posting a 3.03 ERA in a career-high 66 appearances.
Estrada, 29, earned $486,000 last season and was a first-year arbitration-eligible player after going 5-7 with a 3.64 ERA last season.