[6] On July 23, 2015, Kozuka announced his engagement to his girlfriend and Japanese television news presenter, Yukari Oshima.

Kozuka debuted on the ISU Grand Prix of Figure Skating series in the 2006–07 season.

He won the bronze medal at the 2006 NHK Trophy and placed 6th in the 2006 Trophée Eric Bompard.

In the 2008–09 season, Kozuka won gold at the 2008 Skate America and silver at the 2008 Trophee Eric Bompard.

In the 2009–10 season, Kozuka won the silver medal at the 2009 Cup of Russia earning 215.13 points and placed seventh in the 2009 NHK Trophy scoring 186.00.

Kozuka's assigned events for the 2010–11 ISU Grand Prix season were the 2010 Cup of China and the 2010 Trophée Eric Bompard.

During a practice session at the Grand Prix Final, Kozuka inadvertently collided with Daisuke Takahashi.

"[16] Kozuka was fourth in the short program and second in the free skate, and won the bronze medal.

He won his first national title in December 2010, placing first in both the short program and the free skate to total 251.93 points.

Kozuka began the 2012–13 season by winning gold at the 2012 Skate America and then won silver at the 2012 Rostelecom Cup.

When Daisuke Takahashi withdrew from the 2014 World Championships, Kozuka replaced him as a substitute and placed 6th at that competition.

[6] On April 17, he performed his farewell exhibition program, Epilogue, at the last show of 2016 Stars on Ice Japan in Tokyo.