The finalized deal is pending a physical.
Duensing, 34, went 1-1 with a 2.74 ERA in 68 appearances with the Cubs last season and is 43-38 with a 4.01 ERA in 436 major league appearances. Duensing spent his first seven seasons with the Minnesota Twins and was in the minors for much of 2016 before being called up by the Baltimore Orioles late in the season.
Duensing is a former third-round draft pick by the Twins in 2005 and made his major league debut in 2009.
--The New York Mets are likely to begin the season without All-Star outfielder Michael Conforto, as general manager Sandy Alderson told reporters that the 24-year-old is on track to return from shoulder surgery in early May.
"Conforto probably will not be ready," Alderson said. "Everything's going as planned. There have been no setbacks. But his schedule is such that I don't expect him back until the first of May."
Conforto had surgery in September after dislocating his left shoulder on a swing during a game against the Arizona Diamondbacks on Aug. 24. The injury ended what was a breakout season for Conforto, who hit .279/.384/.555 with 27 home runs and 68 RBIs in earning his first career All-Star selection.
Jeffress was sentenced to three days in jail, according to Dallas County District Court, after pleading guilty on Tuesday. He was credited with time served and will do no further jail time.
Jeffress was arrested by Dallas police on Aug. 26, 2016, when he was a member of the Texas Rangers. Texas traded Jeffress back to the Brewers last July 31 at the trading deadline. The Rangers had acquired him from Milwaukee at the 2016 trading deadline.
--Field Level Media