Rodriguez, a 14-time All-Star with 13 Gold Gloves, has agreed to a two-year, $5 million deal with the Nats, sources confirmed to ESPN The Magazine's Buster Olney. He turned down arbitration from the Rangers.
The agreement was first reported by MLB.com.
The Associated Press reported that the deal is subject to the 38-year-old passing a physical.
Rodriguez was acquired by the Rangers in August last season, serving his second stint with the team on which he became a star. He made 10 All-Star Games and won an MVP with the Rangers from 1991-2002.
He went on to play on the Marlins championship team in 2003 and then spent over four seasons with the Tigers. In the past few seasons he has bounced around, from the Yankees to the Astros and back to the Rangers.
He batted .249 with 10 home runs and 47 RBIs last season. He has a .299 career batting average.
Flores was injured May 9 when he was hit by a foul ball, returned for three at-bats in early September, then had surgery to repair a torn labrum. He hit .301 with four homers and 15 RBIs in 93 at-bats. He is expected to be the starter.
Earlier in the day the Nationals acquired right-handed reliever Brian Bruney from the Yankees for a player to be named.
Information from The Associated Press was used in this report.