Foxsports.com and CBSSports.com were the first to report Cincinnati's agreement with the free-agent outfielder.
The person spoke to The Associated Press on condition of anonymity Monday night because the deal was pending a physical and no announcement had been made by the team.
An all-star in 2008 with St. Louis, the 33-year-old Ludwick was traded from San Diego to Pittsburgh at the July 31 deadline last season. He batted a combined .237 with 13 homers and 75 RBIs.
Ludwick could give the Reds the right-handed bat they've been seeking to complement lefty sluggers Joey Votto and Jay Bruce. He figures to see playing time in left field, a spot filled mostly by Chris Heisey down the stretch last season after Cincinnati traded Jonny Gomes to Washington in late July.
It's the latest move in a busy off-season for the aggressive Reds, who had previously been focused on pitching. Cincinnati acquired starter Mat Latos and left-handed reliever Sean Marshall in separate trades before reaching an oral agreement on an $8.5 million, one-year contract with free-agent closer Ryan Madson.
Ludwick had a $6,775,000 salary last year.