Dotel's deal allows him to earn about $2.5 million in performance bonuses based on games finished. The 33-year-old right-hander has missed most of the last 1½ seasons because of an elbow injury.
"I'm going to Kansas City for the physical and then the signing will be official," Dotel told The Associated Press in his native Dominican Republic.
General manager Dayton Moore and Rene Francisco, who oversees international operations for the Royals, met with Dotel a couple weeks ago. Scouts watched him pitch on Wednesday in his season debut with the Escogido Lions in the Dominican Winter League and were impressed.
"He was outstanding," Moore said. "He threw the ball very well. Before his injuries, he was one of the premier relief pitchers in the game. We expect him to have a great year closing out games for us."
He had elbow ligament replacement surgery in June 2005 and returned in mid-August but was largely ineffective, going 0-0 with a 10.80 ERA for the Yankees. In 14 appearances, he allowed 13 runs, 18 hits and 11 walks in 10 innings.
He saved a career-high 36 games in 2004 with the Astros and A's.
"I feel very happy because of the confidence the Royals have shown in me," said Dotel, who picked the Royals over the Yankees, Boston Red Sox and Tampa Bay Devil Rays because it gave him the best opportunity to be a closer.
In addition, Kansas City agreed to a $4 million, two-year contract with left-hander John Bale that will pay him $1.8 million next year and $2.2 million in 2008.
The 32-year-old pitched the last three seasons for the Hiroshima Toyo Carp in Japan's Central League, going 1-2 with six saves and a 2.93 ERA in five starts and 34 relief appearances last season. He pitched for parts of four seasons with the Toronto Blue Jays, Baltimore Orioles and Cincinnati Reds.
The Royals have been among the most frugal franchises in recent years when it comes to player payroll. But under Moore, who was hired in June to replace the fired Allard Baird, Kansas City was among the more active clubs at the winter meetings.
Kansas City traded inconsistent right-handed reliever Ambiorix Burgos to the Mets for right-handed starter Brian Bannister and then agreed to a $55 million, five-year deal with right-hander Gil Meche.
"What we've done is fit within our payroll structure," Moore said. "It fits in going forward. What I've said all along is we're going to sign players that will make a difference for us long-term."
Moore said the Royals might make more moves.
Kansas City is targeting free-agent right-hander Miguel Batista, as it continues to build a pitching staff around a talented group of young position players that includes minor-league player of the year Alex Gordon.
"We're continuing to work on things all the time," Moore said. "To try to take this core of position players and expect them to outscore everybody in the major leagues is not a realistic expectation. You have to have the pitching to support your offense.
"We've had great baseball discussion," Moore added. "A lot of creative thinkers, a lot of traditional, sound baseball judgment."