Los Angeles also acquired former World Series MVP pitcher Josh Beckett, injured four-time all-star outfielder Carl Crawford and utility infielder Nick Punto in exchange first baseman James Loney and four minor-league prospects.
The Boston Herald reported the deal had been finalized, and includes the Dodgers receiving $12 million in payments from the Red Sox.
Gonzalez was expected to be in Saturday night's Dodgers lineup against Miami, the team said.
The slugging first baseman, who began his career with the San Diego Padres, wrote on his Twitter account, "Thanks to Red Sox nation for everything. You guys are great! Excited to get back to Cali and be a part of Dodgertown!"
He batted .321 with 42 home runs in 282 games with Boston.
The trade removes about $270 million in financial liability from the payroll of the struggling Red Sox, and indicates the club has switched into full rebuilding mode.
Gonzalez is owed $127 million the next six seasons, while Beckett is owed $31.5 million. Crawford, who underwent reconstructive elbow surgery last week, has $102.5 million coming over five seasons.
The Dodgers are vying with the San Francisco Giants for the National League West title, while the Red Sox are mired six games under .500 and have been wracked by dissent under Manager Bobby Valentine.
Minor-leaguer infielder Ivan DeJesus Jr. and right-handed pitcher Allen Webster were shipped to Boston, along with two prospects to be named later.