Yoriyuki, the son of the noted warrior-scholar Hosokawa Yoriharu, was a loyal and talented supporter of the Ashikaga. He served as the first Kanrei (Deputy/Vice-shôgun) and acted as guardian and counsel to Ashikaga Yoshimitsu. At the same time he expanded and consolidated the Hosokawa influence over Awa and Sanuki on the island of Shikoku, provinces that would be Hosokawa bastions until the 16th Century.
As Kanrei Yoriyuki sought to avoid creating another version of the Hojo Shikken and instituted a policy whereby posting as Kanrei was alternated between the Hosokawa, Shiba, and Hatakeyama shugo families. This did not stop other lords from becoming jealous of Yoriyuki's closeness of the shôgun. After a 12-year tenure as Kanrei, Yoriyuki was forced to step down, costing the Ashikaga an almost indispensable asset.
A marked contrast to later Hosokawa Kanrei, Yoriyuki is little known but epitomized the soldier-statesman ideal so cherished during the early to mid-Muromachi period.