Kubiak started his coaching career at Texas A&M University as an offensive quality control coach from 2010 to 2011 and as a graduate assistant and inside receivers coach in 2012. During his three years with the Aggies, Kubiak earned his master's degree in human resource development.
In 2013, Kubiak was hired by the Minnesota Vikings as an offensive quality control and assistant wide receivers coach under offensive coordinators Bill Musgrave (2013) and Norv Turner (2014).
In 2015, Kubiak accepted a position at the University of Kansas to coach the wide receivers.
On February 22, 2016, Kubiak was hired by the Denver Broncos as an offensive assistant while his father, Gary Kubiak, was the head coach of the team. During the 2017 season, Kubiak assumed responsibilities as the primary quarterbacks coach for the final six weeks of the regular season after Bill Musgrave was promoted to offensive coordinator.
On January 14, 2019, Kubiak was hired by the Minnesota Vikings as their quarterbacks coach under offensive coordinator Kevin Stefanski and head coach Mike Zimmer.

On February 8, 2021, Kubiak was promoted to offensive coordinator, replacing his father, Gary Kubiak, following his retirement.
On February 2, 2022, Kubiak was re-hired by the Denver Broncos as their passing game coordinator and quarterbacks coach under offensive coordinator Justin Outten and head coach Nathaniel Hackett. Following offensive struggles to start the 2022 season, Hackett relinquished play calling duties to Kubiak on November 20.
On March 23, 2023, Kubiak was hired by the San Francisco 49ers as their passing game coordinator.
On February 14, 2024, the New Orleans Saints hired Kubiak to be their new offensive coordinator for the 2024 season, replacing the Saints' longtime offensive coordinator Pete Carmichael Jr.
On January 26, 2025, the Seattle Seahawks hired Kubiak as their new offensive coordinator.

Klint is the oldest son of former NFL coach Gary Kubiak. He has two younger brothers, Klay, the offensive coordinator for the San Francisco 49ers, and Klein, a national scout for the Dallas Cowboys.

• Seattle Seahawks profile
• Colorado State Rams profile