Sources told ESPN The Magazine's Buster Olney the Rockies will save $1.1 million in salary in the deal.
The trade features two once-promising but now-struggling pitchers.
Guthrie had double-digit victories in three straight seasons with the Baltimore Orioles in the American League.
Sanchez threw a no-hitter for the San Francisco Giants and was a part of the Giants' 2010 World Series rotation.
Guthrie opened this season with the Rockies and Sanchez with the Royals, but both struggled in their new leagues.
"I'm excited," Guthrie said. "The first thought is disappointment that I couldn't hold up my end of the bargain in Colorado and help that team win games, which I think they were built to do at the start of this year.
"But as I looked at what was in my future and I look at the Royals, I see a perfect fit there. I'm excited to play with the guys that are down there. It's a young core of great baseball players and an organization that has been lauded recently for the moves and the progress they've made, and I really hope to come in there and be a large part of good things that we can do here in the near future."
Sanchez was designated for assignment Tuesday by the Royals. The 29-year-old left-hander is 1-6 with a 7.76 ERA in 12 starts this season. A seven-year major league veteran, he is 39-52 with a 4.50 ERA, 420 walks and 772 strikeouts in 186 games (130 starts).
Sanchez threw a no-hitter against San Diego in 2009 and the Royals traded away Melky Cabrera to get him last November in what turned out to be one of the worst trades in team history. Sanchez was winless in his final 11 starts with Kansas City. Cabrera was named MVP of the All-Star Game earlier this month.
Guthrie, a 2002 first-round pick of the Cleveland Indians, was the Orioles' Opening Day starter from 2008-10, and surpassed the 200-inning mark in each of the past three seasons.
He is scheduled to make his first Royals' start Sunday against the Twins. The Royals' rotation has a 26-40 record with a 5.43 ERA and has worked the fewest innings, 467 2/3, of any major league rotation this season.
"I'm looking to hopefully being a workhorse, someone that can go out there and be there for the team whenever he's needed," Guthrie said. "I have been blessed with a lot of health in my career, which is really important: to be able to go out there and your team can depend on you, to go out there and throw the innings and give them a chance to win."
Information from The Associated Press was used in this report.