Wood was drafted in the third round of the 2006 Major League Baseball Draft by the Royals, and he began his professional career that season. Playing for the Idaho Falls Chukars, he went 3-1 with a 4.50 ERA in 12 starts. He pitched for three teams in 2007 - the AZL Royals, the Burlington Bees and the Wilmington Blue Rocks - going a combined 2-2 with a 2.78 ERA in 13 starts. In 2008, Wood pitched for the Blue Rocks and Northwest Arkansas Naturals, going a combined 8-9 with a 4.25 ERA in 28 starts. In 144 innings, he allowed only 128 hits. Though he spent three games with the AZL Royals in 2009, he spent most of the season with the Naturals, going 2-8 with a 5.83 ERA in 17 games with them. Overall, he went 2-9 with a 5.55 ERA in 2009. Wood made his MLB debut for the Royals on May 12, 2010. Wood went 6-6 with a 4.30 ERA in 106 appearances in two seasons with the Royals. On May 18, 2012, it was announced that Wood's 2012 season has ended due to a torn UCL in his right elbow, requiring Tommy John surgery.
Cleveland Indians
On November 2, 2012, Wood was claimed off waivers by the Cleveland Indians. Wood was activated from the 60-day disabled list on July 14, 2013, and optioned to the Triple-A Columbus Clippers. On December 2, 2013, Wood signed a one-year Major League deal for 2014 with the Indians, avoiding arbitration. On May 26, 2014 the Indians designated Wood for assignment.
Wood signed a minor league deal with the Pittsburgh Pirates on November 18, 2014. He was named a Triple-A All-Star with the Indianapolis Indians. for the Indians in 2015
Cincinnati Reds
On November 20, 2015, Wood signed a one-year deal with the Cincinnati Reds. Wood would enjoy the best season of his career, appearing in 70 games with a 3.99 ERA. He was designated for assignment on August 23, 2017. His 2017 season ended with a 5.65 ERA in 55 games for the Reds.
Los Angeles Angels
On August 25, 2017, Wood was claimed off waivers by the Los Angeles Angels. He continued for the remainder of the season in the Angels bullpen, appearing in 17 games. The Angels re-signed Wood to a 1 year deal after the season. On May 29, 2018, Wood was diagnosed with a UCL tear, requiring him to miss the remainder of the season and the beginning of the 2019 season while he undergoes Tommy John surgery.
