Hosoda was born in Kamiichi, Nakaniikawa District, Toyama, Japan. His father worked as a railway engineer, and his mother was a tailor.
Hosoda was strongly influenced by the animation works he saw in 1979, when he was in the sixth grade, and set his sights on a career related to anime. These were Isao Takahata's Anne of Green Gables, Osamu Dezaki's Aim for the Ace! The Movie and Yoshiyuki Tomino's Mobile Suit Gundam, Rintaro's Galaxy Express 999 The Movie and Hayao Miyazaki's Lupin III: The Castle of Cagliostro. Hosoda described the concentration of works in that one year that would go down in Japanese animation history as like a Grand cross (the planets of the solar system lining up in a cross on the ecliptic). Hosoda had already analyzed the directing methods and screen compositions of Hayao Miyazaki and Rintaro in a collection of essays written by elementary school graduates. Hosoda cited Isao Takahata's Anne of Green Gables as the most influential anime of them all. He says that Takahata, as a 'director who does not draw', taught him that drawing is not the only way to dominate a film.
When Hosoda was in junior high school, he saw people his age making animation on NHK Educational TV's independent animation specials, and he started making paper animation using the anime magazine Animage as a reference. Hosoda applied as a first-year high school student for the open call for animators for the Toei Dōga-produced film Shōnen Kenya (1984) and was shortlisted, but withdrew because of mid-term exams.
He majored in oil painting at the Kanazawa College of Art in Ishikawa Prefecture. He then joined the film club at that college and produced live-action films, somewhat distancing himself from animation. Hosoda produced nearly 50 video works: two fiction films were submitted to the Pia Film Festival and the Image Forum Festival, among others, and he also produced other video art works.
In 1989, Hosoda saw an article in Animage recruiting trainees for the production of Studio Ghibli's Only Yesterday (1991 film) and took a recruitment test. Although he did not pass the exam, he received a letter from Hayao Miyazaki saying that he had decided not to hire someone like you because he thought it would diminish your talent.
After graduating from university, Hosoda continued to look for work in the animation industry and contacted a producer with whom he had formed a connection during an open call for animators for Shōnen Kenya, and joined Toei Dōga (recently Toei Animation) in 1991. He had initially wanted to pursue a directing course, but following that producer's recommendation, he ended up working as an animator for the time being.