Arizona receives relief pitching prospect Andrew Hoffmann as part of the deal.
The trade occurred while Grichuck was playing mid-game against the Pittsburgh Pirates before teammate Jorge Barrosa pinch-hit for him after the deal was done.
Grichuk will now be heading to his sixth team in 12 years as the Royals (51-53) try to make a Wild Card push for this season.
The 33-year-old righty is slashing .243/.280/.462 this season with seven home runs and 22 RBI in 69 games.
Grichuck is currently on a one-year deal worth $5 million with a mutual option for 2026.
As for Hoffman, the 25-year-old has appeared in three games for the Royals this season, throwing a 3.86 earned run average through seven innings.
In Triple-A this year, Hoffman posted a 2.25 ERA with 55 strikeouts in 40 innings.