Kobayashi studied computer science at Chukyo University. After graduating, he was hired at Capcom in 1995 as a programmer on the first Resident Evil game. After working as programmer on the sequel and a planner on the first Dino Crisis game, his first producer role was on Dino Crisis 2 in 2000.
Starting with the first Sengoku Basara game (titled Devil Kings in North America) in 2005, Kobayashi worked as the producer for the video game series as well as a planning supervisor for the various anime adaptations. He was very interested in the Sengoku period and wanted to create an action game inspired by that period.
Kobayashi has worked on a number of video games, including the following (dates given are for the Japanese release). Credits are for producer unless otherwise indicated.
- Resident Evil (programmer, 1996)
- Resident Evil 2 (programmer, 1998)
- Dino Crisis (planner, 1999)
- Dino Crisis 2 (2000)
- Devil May Cry (programmer, 2001)
- Resident Evil 0 (promotional producer, 2002)
- P.N.03 (2003)
- Resident Evil 4 (2005)
- Killer7 (2005)
- Sengoku Basara (2005)
- Sengoku Basara 2 (2006)
- Sengoku Basara 2 Heroes (2007)
- Devil May Cry 4 (2008)
- Sengoku Basara X (2008)
- Sengoku Basara: Battle Heroes (2009)
- Sengoku Basara: Samurai Heroes (2010)
- Sengoku Basara Chronicle Heroes (2011)
- Dragon's Dogma (2012)
- Resident Evil 6 (2012)
Kobayashi has also worked on several anime series.
- Devil May Cry: The Animated Series (TV anime, supervisor, 2007)
- Resident Evil: Degeneration (CG anime film, producer, 2008)
- Sengoku Basara: Samurai Kings (TV anime, planning supervisor, 2009)
- Sengoku Basara II (TV anime, planning supervisor, 2010)
- Sengoku Basara: The Last Party (anime film, planning supervisor, 2011)
- Resident Evil: Infinite Darkness (2021)
- インタビュー 小林裕幸さん. Sony Computer Entertainment (October 2006). Archived from the original on August 9, 2011. Retrieved on August 9, 2011.
- インタビュー ： 「ＰＳＰ版は集大成」 「戦国ＢＡＳＡＲＡ」シリーズの小林裕幸プロデューサー. Mantan Web (May 6, 2009). Archived from the original on August 9, 2011. Retrieved on August 9, 2011.
- Resident Evil Archives II. BradyGames. p. 238.