At the just-completed winter meetings in San Diego, Rangers general manager Jon Daniels said the team was going to sign a right-handed reliever but the deal wouldn't be finished until next week.
Fujikawa must pass a physical, and the club must clear a spot on the 40-man roster before the deal can be final.
Fujikawa pitched for the Chicago Cubs the past two seasons, appearing in 27 games; Chicago declined a $5.5 million club option this offseason. The 34-year-old underwent Tommy John surgery in 2013.
Fujikawa pitched in the final two months of the 2014 season for the Cubs, appearing in 15 games. He finished with a 4.85 ERA and 17 strikeouts to 6 walks.