The Reds are sending pitcher Homer Bailey and prospects Josiah Gray and Jeter Downs to the Dodgers. Kyle Farmer is also headed to the Reds in the trade.
The teams announced the swap on Friday.
Puig, 28, hit .267 with 23 home runs and 63 RBIs in 125 games last season for the Dodgers. The six-year veteran owns a career .279 batting average and has 108 home runs. Puig was an All-Star in 2014. He is eligible for arbitration in 2019.
Wood, 27, posted a 3.68 ERA and was 907 in 33 games last season for the Dodgers. The 2017 All-Star owns a career 3.29 ERA and a 52-40 record in six seasons. The left-handed pitcher was 16-3 in 2017, leading baseball with an 84.2 percent winning percentage. Wood is also eligible for arbitration this offseason.
Kemp is a three-time All-Star and 13-year veteran. The 34-year-old outfielder hit .290 with 21 home runs and 85 RBIs in 146 games last season for the Dodgers. Kemp began his career with the Dodgers in 2006, before joining the San Diego Padres in 2015. He spent time with the Atlanta Braves before rejoining the Dodgers in a December 2017 trade.
Farmer, 28, had nine RBIs and hit .235 in 39 games last season for Los Angeles. The infielder posted a .250 batting average in two seasons with the Dodgers.
Bailey, 32, was 1-14 last season with a 6.09 ERA. The 12-year veteran is due $23 million in 2019 and has a $25 million mutual option in 2020 with a $5 million buyout. The right-handed pitcher owns a career 4.56 ERA and a 67-77 record in 212 career appearances.
Downs is the Reds' No. 7 prospect, while Gray is the franchise's No. 20 prospect, according to MLB Pipeline.