Torre's hiring comes a week after he rejected a reduced monetary and short-term offer to continue managing the New York Yankees, and just days after the Dodgers and former skipper Grady Little parted ways in an awkward split.
Reports said the Dodgers spoke of negotiating with Torre while Little was still under contract.
"Few managers in the history of the game have accomplished what Joe has delivered," said Dodgers General Manager Ned Colletti. "Throughout his career he has demonstrated the ability to turn a vision for success into results on the field and we welcome his passion and leadership."
The Dodgers disappointed last season with an 82-80 record, good for fourth place in the National League West, while the Yankees lost in the first round of the American League playoffs for the third consecutive season.
Torre, 67, who guided the Yankees to four World Championships and 12 straight post-season appearances, will be introduced at a news conference Monday at Dodger Stadium.