The deal is for three years plus a club option and is worth $21 million guaranteed. An announcement is expected Wednesday.
Broxton is expected to be the Reds closer, enabling them to move the 100-mph-throwing Aroldis Chapman to the rotation.
Broxton proved to be a versatile reliever in his time in Cincinnati, but he should be back as the ninth-inning guy. Broxton was 4-5 with 27 saves and a 2.48 ERA in 2012 for the Royals and Reds.
Ken Rosenthal of FoxSports.com first reported the sides were closing in on a deal.