The left-handed throwing Wood, who turns 25 in February, was 11-10 with a 4.18 ERA in parts of two major league seasons with the Reds. He was a second-round pick in 2005. Wood may be the Cubs' only left-handed starter next season.
"He caught the eye of a lot of people and a lot of clubs had interest in him," Cubs president of baseball operations Theo Epstein said of Wood. "He's a really athletic package. Very athletic, his arm works very well. More than enough velocity to succeed as a left-handed pitcher.
"Some days you can see him, he has 3 or 4 above-average pitches. Those are the ingredients you need to be successful as a starting pitcher."
Wood made 17 starts for the Reds in 2010, going 5-4 with a 3.51 earned run average. He took a perfect game into the ninth inning against the Philadelphia Phillies before giving up a double to Carlos Ruiz, and left after finishing the 9th with the score tied at 0.
He began last season in the Reds' starting rotation, made 10 starts for Louisville, then returned to Cincinnati. He also had four relief appearances for the Reds last season.
"He had a little bit of a down year last year, a little bit of a sophomore slump, but we still think all the ingredients are there to make him an excellent starting pitcher in the big leagues and you tend to not be able to get guys like that after their strong rookie years," Epstein said. "But sometimes you have a chance to get them after they take a little bit of their lumps on the learning curve."
Wood said he relied too heavily on his cutter last season and "lost the ability to really stick that four-seam (fastball) in there." His control was off, but he also sees a shot at redemption in Chicago.
"I think it's a great opportunity for me," he said. "The Reds do have a lot of depth in their rotation. ... Hopefully, I can get to Chicago and make a difference."
Besides the addition of Latos, the Reds return starting pitchers Johnny Cueto, Mike Leake, Homer Bailey and Bronson Arroyo. Aroldis Chapman, a left-handed reliever in his first two seasons, is also a possible starting pitcher next season.
Epstein also said the Cubs aren't done making moves.
"I don't think we are done," he said. "I do think we still need to build more depth on the starting pitching front, both in the big leagues and minor leagues. But it doesn't happen overnight. You have to make sacrifices. Just like moving Sean Marshall, who was certainly an asset for the 2012 club."
Outfielder Dave Sappelt and minor league infielder Ronald Torreyes were the other two involved in the trade.
Sappelt, who turns 25 in January, was Cincinnati's minor league hitter of the year and the Southern League's MVP in 2010. He made his major league debut against the Cubs in Wrigley Field and batted .243 with eight doubles and 14 runs in 38 major league games.
The 19-year-old Torreyes batted .364 with 38 doubles in the minors last season.
Marshall, 29, was one of the top left-handed relief pitchers in the majors last season. He went 6-6 with five saves and a 2.26 ERA in 79 relief appearances. He had 34 holds, which was a club record and third-highest total in the majors.
"Sean has been one of the best and most durable relievers in baseball the last couple of seasons," Reds general manager Walt Jocketty said in a statement.
In another move, Cincinnati claimed reliever Josh Judy off waivers from Cleveland. The 25-year-old right-hander pitched in 12 games over four stints with the Indians last season, with no record and a 7.70 ERA. He was 6-2 with a 3.12 ERA and 23 saves at Triple-A Columbus.
ESPNChicago.com's Bruce Levine and The Associated Press contributed to this report.