The deal is for two years and worth $8 million guaranteed, with a club option for a third year, a source told ESPN's Jeff Passan.
The 34-year-old Jones hit .260 with 16 home runs and 67 RBIs with Arizona this past season.
"It's that time in my career and life my family and I had to make a HUGE decision, and so that is what we have done!!! MLB has been amazing to myself and my family," Jones wrote on Twitter. "We had an incredible run from the day I signed in 2003 to my final AB last year. It's been the greatest 12 years and 139 days a person could ask for!"
Orix plays in Nippon Professional Baseball and has four Japan Series championships, with the most recent coming in 1996.
"[Orix] views me as a valuable piece to help bring their organization back on track and I'm up for the challenge!!" Jones wrote. "They have expressed to my family and I that they value everything I bring to the game, and have proven that."
Jones began his career with the Seattle Mariners before being traded to Baltimore, where he spent 11 seasons. The five-time All-Star and four-time Gold Glove winner has 282 career home runs with 945 RBIs.