The contract is not finalized yet, but it will include an invitation to big league spring training, per the source.
Carroll, who will turn 40 next month, has played in 12 big league seasons and has experience playing second base, third base and shortstop. He played with the Nationals during their inaugural season in D.C. in 2005, and suited up for both the Twins and Royals last season.
He's posted a career slash line of .272/.349/.338, but hit just .211/.267/.251 in 249 plate appearances in 2013.
Carroll will compete with Danny Espinosa and Zach Walters for a backup infielder job on the Nationals' roster. Will Rhymes is another option; he re-signed with the Nats in December on a minor league deal.
Espinosa had been the clear favorite to earn a spot on the Nats' bench as a reserve option at second base and shortstop (and possibly even third base) in 2014, but Carroll provides clear competition as a respected veteran presence who is capable at multiple positions defensively and who has has the ability to get on base at a solid clip in past seasons.
One factor that might work in Carroll's favor is the success that he's had in his career in a pinch-hitting role; he's got a career .339 average and .417 on-base percentage over 146 pinch-hit plate appearances.
In his age-40 season, it's unclear how much Carroll has left in the tank, but we'll get a look in spring training when he'll again toss on a Nationals jersey and battle Espinosa for a spot on the Nats' opening day roster.
MLB Daily Dish was the first to report the Nats reaching a deal with Carroll.
Update: The Nationals have yet to formally announce the Carroll deal, but they did announce this afternoon that they've signed Mike Fontenot to a minor league contract, further bolstering their infield depth.
Fontenot's deal contains an invitation to big league spring training.
The 33-year-old Fontenot is a left-handed hitter who has played the bulk of his career at second base. He also has experience at shortstop and third base.
Fontenot has a career .265/.332/.401 slash line over seven big league seasons, spent with the Cubs, Giants and Phillies.
He didn't play in the majors in 2013, but hit .264/.335/.379 with four homers and 42 RBIs with Triple-A Durham in the Rays organization.
Add another middle infield option to the mix.