The team on Thursday also signed right-hander Kris Medlen to a two-year contract with a mutual option for 2017. Medlen, who was not offered a contract by the Atlanta Braves after undergoing Tommy John surgery last season, was 15-12 with a 3.11 ERA in 2013 for Atlanta.
The Royals have been busy since last week's winter meetings, agreeing to deals with outfielder Alex Rios and first baseman Kendrys Morales to bolster the lineup and now Volquez, who likely will take James Shields' spot in the rotation. Shields, who remains a free agent, isn't expected to re-sign with the team.
Volquez, 31, went 13-7 with a 3.04 ERA in 31 starts last season, his first with the Pittsburgh Pirates.
After a down year in 2013 with the Padres and Dodgers (9-12, 5.71 ERA), Volquez bounced back in Pittsburgh. His 3.04 ERA ranked 11th among National League right-handers last season.
He was paid $5 million in 2014.