The person spoke Saturday under condition of anonymity because there was no official announcement about the agreement.
The 34-year-old Ludwick hit .275 with 26 home runs and 80 RBIs while helping Cincinnati win the NL Central. He hit three homers and batted .333 in the Reds' five-game loss to San Francisco in the NL division series.
Ludwick declined a mutual option after the season, turning down a $5 million salary and instead receiving a $500,000 buyout. He had signed a one-year deal with a $2 million base salary for 2012, and earned another $350,000 in performance bonuses based on plate appearances.