Chris Cotillo of SB Nation was the first to report the signing.
Culberson, who turns 27 in April, was sidelined for almost all of the 2015 season with a bulging disc injury in his back. He didn't play in the majors all season and was limited to just five games with Triple-A Albuquerque in June. The Rockies sent him outright to Triple-A in June, removing Culberson from the 40-man roster. He became a minor league free agent after the season.
The right-hander hit .221/.265/.314 in parts of three seasons from 2012-14 with the Giants and Rockies. He played over half of his games in the minors at second base, but also saw significant time at shortstop and third base. In the majors, Culberson has started 20 games at second base, 18 at third base, 14 games at shortstop, three games at first base and even 20 games in left field.
San Francisco originally drafted Culberson in the supplemental first round in 2007, with the 51st overall pick.
Should Culberson find his way to the Dodgers' 40-man roster, he does have one option year remaining, having been optioned in both 2012 and 2013. Culberson was also optioned in 2014, but the assignment lasted just eight days, far less than the 20 total days on optional assignment in one season to count as an option year.
The Dodgers haven't yet announced reporting dates for 2016 spring training, but their Cactus League schedule begins on Thursday, March 3.