Randolph grew up in Marion, Indiana and attended Marion High School, where his coach was Moe Smedley. Zach was mentored by Craig Moore, a teacher at Marion, since he was 12. They are still great friends today. As a sophomore, he helped lead the Marion Giants to the class 4A championship game. As a senior, he again led his team to the state championship game in which Marion High School won its seventh state basketball championship. He finished second in Indiana's 'Mr. Basketball' voting that year, closely behind Jared Jeffries, who coincidentally played for the team that the Giants beat in the state championship game that year and would later become Randolph's teammate with the Knicks.
He was drafted by the Blazers in the first round (19th overall) in 2001. He plays the power forward position. In 2004 he won the NBA's Most Improved Player award, after which he signed a 6-year, 84-million dollar extension with the Blazers. Randolph averaged 23.6 points and 10.1 rebounds per game in the 2006-07 season, which was cut short in March of 2007 due to a hand injury. In his final game as a Trail Blazer, he had 43 points and 17 rebounds.