Uggla will be assigned to Triple-A Fresno, according to the source.
The move came three days after Uggla was released by the Atlanta Braves.
Fox Sports reported Uggla's deal with the Giants earlier Monday.
In his fourth season with the Braves, Uggla, 34, was batting .162 with two home runs and 10 RBIs in 48 games and 130 at-bats.
He had a 33-game hitting streak in 2011, the franchise's second-longest, but also struck out 495 times in 451 games from 2011 to 2013.
Uggla, a three-time NL All-Star, hit .179 with 22 homers and 55 RBIs last year and underwent corrective eye surgery last summer. He struggled so much that he was left off the postseason roster after losing his job to Elliot Johnson, a journeyman claimed off waivers in late August.
The Braves reinserted Uggla as the starter at the beginning of spring training this year, but he hit .212 in April and .080 in 25 at-bats during May.
The Associated Press contributed to this report.