The deal is worth $12 million, a person familiar with the negotiations told The Associated Press on condition of anonymity earlier this week.
The 30-year-old Wood made a career-high 77 appearances with the Chicago Cubs last season, posting a 4-0 record and a 2.95 ERA. He held lefties to a .128 average.
A 2013 National League All-Star, Wood spent the last five seasons with the Cubs after arriving in a trade with Cincinnati in 2011. He owns a career record of 43-52 with a 4.00 ERA in 259 games (133 starts). Since transitioning to the bullpen in 2015, he’s 7-2 with a 2.95 ERA in 122 appearances.
The Royals also placed pitcher Brian Flynn on the 60-day disabled list with a back injury.