He attended Notre Dame High School in Milwaukee, where he was a standout basketball player.

[2][5] He could also score, averaging 20.9 and 21.4 points per game in his junior and senior years; and was the school's all-time scorer when he graduated.

[3] In 1963, he was captain of the United States men's national basketball team at the 1963 FIBA World Championship that came in fourth place.

He was also captain of the U.S. team that won the Gold Medal at the 1963 Pan American Games a few weeks earlier.

[11] He also played for the Detroit Pistons (1964–66), Chicago Bulls (1966–67) (acquired prior to the season via the expansion draft), San Diego Rockets (1967–70) (acquired prior to the 1967–68 season via the expansion draft), Seattle SuperSonics (1970–72) and Kansas City-Omaha Kings (1972–75).

[15] In his first year with the Bulls, Kojis played with future Naismith Hall of Fame point guard Guy Rodgers, who was known for his exceptional passing.

[18] Rodgers and Kojis worked together and "introduced the back door baseline lob slam dunk to the NBA", which became the team's most popular play that year in Chicago.

[12] He was named to the 1968 and 1969 NBA West All-Star Teams, as a San Diego Rocket, and was a starter in the 1969 game.

Kojis resided in the San Diego County community of Julian, California and was the director of Whispering Winds Catholic Conference Center for 34 years, serving hundreds of thousands of people over that time.