Guerrero, 26, batted .290 with 21 home runs and 51 RBI in 80 games last season, his seventh with the Las Tunas Magos of the Cuban National Series.
A shortstop with a .977 fielding percentage, Guerrero defected from this year and has since been working out in the Dominican Republic.
Terms of the deal weren't announced, but the Los Angeles Times reported it is worth $28 million on top of a $10 million signing bonus.
"We feel Alexander can be an offensive infielder and a solid everyday player," Dodgers General Manager Ned Colletti said. "We're looking forward to him competing for a middle infield position and becoming a key contributor in 2014."