Anthony Erwin Randolph, Jr. was born to Anthony and Crystal Randolph in Würzburg, West Germany, where both of his parents served in the military. Randolph spent the first year of his life in Germany before his family moved to Pasadena, California, where he spent the majority of his childhood. Randolph attended schools in Pasadena as well as North Little Rock High School in North Little Rock, Arkansas, before heading to Woodrow Wilson High School in Dallas, Texas, for his junior year.
Randolph's mother decided the school he was attending in Arkansas was not right for him because of the differences he had with the coach and in school. At the time he was a virtually unknown player. Pat Washington, Randolph's high school coach, stated that while Randolph was athletically gifted, he needed a lot of work on skills such as ball handling, shooting, etc. Washington also spoke of a technique the team had in workouts called the "LAB", where the basic rules were that all players in play were required to never stop running under any circumstances, and if the ball was turned over at any point, the player was to run back on defense immediately. The technique might have contributed to Randolph's later defensive prowess, as he has been known to hustle back after turnovers for defensive stops in his professional career.
In high school, Randolph played all five positions on the floor. During his senior season, Randolph's team did not qualify for a playoff position, which coach Washington attributed to bad chemistry. Washington called the team very talented and referred to Randolph as the best player on the roster but stated that "as time went by jealousy and agendas set in and took over." Randolph averaged 25.8 points and 12.6 rebounds as a senior. Although Randolph was named to the first team All-Area The Dallas Morning News boys basketball team, played in the Reebok Round Ball Classic in Chicago and the Adidas Derby Festival Classic in Kentucky (leading all scorers in both games), he was not chosen to play in the McDonald's All-American Game his senior year. Considered a five-star recruit by Rivals.com, Randolph was listed as the No. 4 small forward and the No. 12 player in the nation in 2007.
Glen "Big Baby" Davis had just left Louisiana State University's (LSU) basketball team as well as seven-foot center Magnum Rolle, who transferred to Louisiana Tech, leaving the team with only two bigs, one being a junior college transfer. Due to this fact, LSU told Randolph that if he joined their team, he could possibly play right away as a freshman. Washington said that Baylor, Georgetown, Kansas, Memphis, and Texas were also interested in recruiting Randolph. Though Memphis was Randolph's early choice in the recruitment process, he wanted to attend a school where he could play big minutes, which he figured he probably would not get to do at Memphis since the team's roster was so deep at the time. Randolph made an impact in college right away, as he had six blocks in just his third game during his freshman season. During his lone season at LSU, Randolph earned Honorable Mention All-SEC and First Team All-Freshman Team honors. Randolph was the only LSU Tiger to start all thirty-one games in his freshman season, and averaged 15.6 points, 8.5 rebounds, 1.2 assists, 1.13 steals, and 2.26 blocks per contest. Although the team only ended the season with a 13-18 record, Randolph finished strong by averaging 20.1 points during the last nine games of the year. Randolph also ranked third in the Southeastern Conference in rebounding and blocked shots, twelfth in scoring, and posted nine double-doubles his freshman season.
Knowing there was a good chance he would be chosen in the first round, Randolph declared himself eligible for the 2008 NBA draft at the end of his freshman year at LSU. Some projected Randolph to go high in the year's draft because of his versatility and potential, while his detractors thought he might drop because of his thin frame and raw overall game. In either case, many believed Randolph could be the steal of the draft with his talent and tremendous potential.
In the draft, the Golden State Warriors selected Randolph with the fourteenth overall pick. The Warriors were coming off a disappointing 2007-08 season where the team was unable to qualify for the playoffs despite finishing the year with a 48-34 win-loss record. Early in his rookie season, Randolph received minimal playing time, causing some to question his attitude and work ethic, or if a possible rift might be developing between him and head coach Don Nelson. Many of the Warriors' main rotation players suffered injuries throughout Randolph's rookie campaign, and the team ended the season with only a 29-53 record. Nonetheless, the Warriors did play a fairly strong second half of the season, including Randolph, who averaged 13.5 points, 10.5 rebounds, 1.6 blocks, and 1.4 steals over the last twelve games of the year.
After attending a Dallas Mavericks-San Antonio Spurs playoff game during the Warriors' offseason, Randolph became motivated to improve his play, hitting the gym hard to prepare for the following season. Randolph's efforts first began to reward him in that year's Summer League being held in Las Vegas, Nevada where he not only began to dominate consistently but was also referred to by various sportswriters as being the best talent in the entire Summer League. Among other highlights, including a then-Summer League record tying 42-point explosion in game four against the Chicago Bulls' Summer League team, Randolph was invited to attend the USA Basketball Men's National Team mini-camp following his dominant Summer League performance. Though many believed Randolph was a lock to win Summer League MVP, the honor was given to 2009 first overall pick Blake Griffin. On October 14, 2009 the Warriors extended Randolph's contract through the 2010–11 NBA season.
On July 9, 2010, Randolph was traded to the New York Knicks along with Kelenna Azubuike, Ronny Turiaf and a future second-round pick in a sign and trade deal for David Lee.
On February 22, 2011, Randolph was traded to the Minnesota Timberwolves in a three-way blockbuster deal which also involved the Denver Nuggets that brought Carmelo Anthony to New York. In his first start of the year on March 24, filling in for the injured Kevin Love, Randolph recorded a career high 31 points and 13 rebounds. He followed that up with 24 points and 15 rebounds.
On July 20, 2012, Randolph signed a multi-year contract with the Denver Nuggets.
On June 26, 2014, Randolph was traded, along with Doug McDermott, to the Chicago Bulls for Gary Harris, Jusuf Nurkić and a 2015 second-round pick.
On July 14, 2014, he was traded, along with two future second round draft picks and cash considerations, to the Orlando Magic in exchange for the draft rights to forward Milovan Raković. The next day, he was waived by the Magic.
On August 18, 2014, Randolph signed a one-year deal with Lokomotiv Kuban of Russia. On April 16, 2015, he was named to the All-EuroCup Second Team. In July 2015, he re-signed with Lokomotiv. In his second season with Lokomotiv, he reached the 2016 Euroleague Final Four, where his team lost in the semi-finals, but managed to win the third place game.
On July 15, 2016, Randolph signed a one-year deal with Real Madrid. On June 22, 2017, he re-signed with Real Madrid.
On June 23, 2017, it was announced that Randolph would play for the Slovenian national team. On September 17, 2017, they defeated Serbia in the finals with a score of 93–85 and thereby claiming the title of EuroBasket champions. Randolph was an important member of this team and returned to Madrid with a golden medal.
Note: The EuroLeague is not the only competition in which the player participated for the team during the season. He also played in domestic competition, and regional competition if applicable.
Randolph has a younger sister, Ashley, as well as a younger brother, Robert. Randolph has said that he enjoys fishing and is a fan of the Dallas Cowboys.