The Cubs also acquired outfielder Dave Sappelt and minor leaguer Ronald Torreyes.
Wood, who turns 25 in February, split the 2011 season between the Reds and Triple-A Louisville. He went 6-6 with a 4.84 earned run average in 22 games (18 starts) in the majors and compiled a 2-3 record with a 5.33 ERA in 10 minor league starts.
The Arkansas native reached the majors with the Reds in 2010, going 5-4 with a 3.51 ERA in 17 starts.
Sappelt made his major league debut last season and hit .243 in 38 games with the Reds. Cincinnati's 2010 Minor League Hitter of the Year, Sappelt batted .313 with 16 doubles, seven home runs and 29 RBI in 74 games in Triple-A
Torreyes is a 19-year-old infielder who spent 2011 at Single-A Dayton.
The Cubs had been the lone team the 29-year-old Marshall pitched for in the majors. During his six-year stint with the Cubs, he amassed a 32-40 record, seven saves and a 3.96 ERA in 292 games (59 starts). Last season, he went 6-6 with a career-best 2.26 ERA in 78 appearances.