The person spoke Thursday on the condition of anonymity because the deal had not been announced. Several outlets had previously reported the agreement.
The Cubs will be the eighth team in 11 years for the 29-year-old Jackson, who also pitched for the White Sox. He is 70-71 lifetime with a 4.40 ERA. He was 10-11 with a 4.03 ERA for Washington last season.
The Cubs also were trying to reach a deal with pitcher Carlos Villanueva. That would give them seven experienced starters, including newcomers Scott Baker and Scott Feldman and holdovers Matt Garza, Jeff Samardzija and Travis Wood.