ESPN.com's Jeff Passan reported the deal is expected to be for three years once it's finalized.
La Stella spent time with both the Oakland Athletics and Los Angeles Angels last season, slashing .281/.370/.449 with 25 RBI and five home runs in 55 games. He'll now join his third California-based team and remain in the Bay Area a bit longer.
Alex Pavlovic of NBC Sports Bay Area noted La Stella will likely spend most of his time at second base but could form a platoon with Evan Longoria at third throughout the year.
The Giants were mostly in need of a left-handed bat to balance out the lineup. La Stella provides that with plenty of pop.
"Team president of baseball operations Farhan Zaidi has said he always felt the Giants were one left-handed bat short late in the year, and now the Giants appear to have solved that problem," Pavlovic reported. "La Stella had a .903 OPS against right-handed pitchers last season."
MLB's infield free-agent market began heating up Tuesday with La Stella's deal announced shortly after news broke of Marcus Semien joining the Toronto Blue Jays and Andrelton Simmons heading to the Minnesota Twins.
The addition likely means less time at second for Donovan Solano and Mauricio Dubon, both righties who figure to find more opportunities in the outfield this year.