Grant was born in Augusta, Georgia. He and his twin brother, Harvey, grew up in Mitchell, Georgia and attended school in Sparta, Georgia. After he graduated from High School he attended Clemson University, where he was a member of Pi Kappa Alpha.
He was drafted by the Chicago Bulls with the 10th overall pick of the 1987 NBA draft. The 6 ft 10 in (2.08 m) tall power forward/center immediately teamed with fellow draft-day acquisition Scottie Pippen to form the Bulls' forward tandem of the future, although he initially backed up incumbent Charles Oakley, one of the league's premier rebounders and post defenders.
In 1989, Grant moved into the starting lineup when Oakley was traded to the New York Knicks for Center Bill Cartwright. He immediately became the Bulls' main rebounder, and established himself as the Bulls' third scoring option after Michael Jordan and Pippen, forming one of the league's best trios. Grant was noted for his defensive play; he was selected four times for the NBA All-Defensive Team. He helped Chicago win three consecutive NBA championships (1991, 1992, and 1993), securing the third with a last-second block on Kevin Johnson.
After Jordan's first retirement following the 1992–93 season, Grant became the number-two star behind Pippen, and helped the Bulls push the Knicks to seven games in the second-round playoff series before being eliminated. Grant played in the 1994 NBA All-Star Game, posting four Points and eight Rebounds in 17 minutes.
After posting career-bests in scoring (15.1 ppg), rebounding (11.0 rpg), and Assists (3.4 apg), he left the Bulls as a free agent and joined the Orlando Magic, led by Shaquille O'Neal and Penny Hardaway. On May 5, 1995, Grant made the final basket in Boston Garden history in Orlando's series clinching victory over the Boston Celtics. Grant helped the Magic reach the 1995 NBA Finals, where they were swept in four games by the Houston Rockets. Grant spent the next several seasons with the Magic.
He was traded to the Seattle SuperSonics along with 2000 and 2001 2nd round picks for Dale Ellis, Don MacLean, Billy Owens, and rookie Corey Maggette just before start of the 1999–2000 season.
After one year with the Sonics, he was involved in a three-way trade in which Glen Rice of the Los Angeles Lakers was sent to New York, Patrick Ewing of the Knicks was sent to Seattle, and Grant to the defending champion Lakers. He helped them win another championship in the 2000–01 season.
In the offseason, Grant decided to leave Los Angeles and sign back with the Orlando Magic. Grant was cut by the Magic in December 2002 after then-coach Doc Rivers implied Grant was a "cancer" on the team.
Grant chose to retire after getting cut by the Magic. However, he decided to return for another run with the Lakers for the 2003–04 season as a backup to Karl Malone. He then retired permanently following the Lakers' loss to the Detroit Pistons in the 2004 NBA Finals.
Grant has three daughters (Naomi, Maia, and Eva) and one son (Elijah) with his wife Andrea. He has two sons (Horace Jr. and Deon) from a previous relationship, and another daughter (Gianna), from a previous relationship. His identical twin brother, Harvey Grant, also played in the NBA, mainly for the Washington Bullets.
Three of Grant's nephews are also basketball players. Jerai Grant played college basketball for Clemson University and currently plays overseas; Jerian Grant played for the University of Notre Dame Fighting Irish men's basketball team and currently plays for the Chicago Bulls; and Jerami Grant played for the Syracuse University Orange men's basketball team and currently plays for the Oklahoma City Thunder.