Born in Borger, Texas, Anderson grew up in Stinnett, seat of Hutchinson County in the Texas Panhandle, and graduated from Stinnett High School in 1961. A talented multi-sport athlete, he was all-state in football and basketball, placed in the state track meet (hurdles and relay) and played baseball in the summer.
Because of a redshirt year due to academic issues, Anderson was eligible as underclassman for the 1965 NFL Draft, then known as a "future" pick. In 1964 he ran for 966 yards with 3 TD and had 32 catches for 396 yards and 4 TD; Despite being selected by the Packers, he returned for his senior season at Texas Tech in 1965 and led the Red Raiders to an 8-2 regular season and a berth in the Gator Bowl on the afternoon of New Year's Eve. As a senior, he ran for 705 yards with 10 TD and had 60 catches for 797 yards and 7 TD.
Selected the outstanding player for Texas Tech in a ten-point loss to Georgia Tech, Anderson signed his pro contract hours after the game. He selected the Packers over the reportedly higher offer from the Houston Oilers of the AFL. His contract was believed to be a then-record $600,000, exceeding Joe Namath's contract of the previous year.
Though he did not see much playing time as a rookie, he was part of a memorable play. During his second carry in the fourth quarter of Super Bowl I, Anderson's knee knocked out Chiefs defensive back Fred "The Hammer" Williamson, who had been boastful in pre-game interviews. Williamson was carried off on a stretcher.
While with the Packers, Anderson originated the concept of hang time in punting. Until Anderson, punters typically strove for maximum distance, with the NFL's leaders usually averaging 45 or more yards a punt. Punt returns varied, with an average of perhaps 5 yards per return. In 1967, the left-footed Anderson worked instead at punting the ball higher, shortening the distance traveled but increasing the ball's time in the air, allowing better coverage by his team on the punt return. Green Bay punted 66 times that year, 63 of them by Anderson; opponents were able to return only 13 of them for a total of 22 yards, or about 1/3 yard per punt. It was Anderson's coach, Vince Lombardi, who explained the concept to sportswriters who questioned why Lombardi didn't try to find a better punter than Anderson, who averaged only 36.6 yards per punt that year. Lombardi pointed out the lack of return yardage. Other punters soon followed Anderson, working for greater hang time. Eventually the NFL changed its rules governing punt coverage, to restore the ability to return punts.
Following his retirement from the NFL, Anderson spent nearly two decades on the celebrity golf tour. As of 2013, Anderson lives in the Dallas area and stays busy with eight grandchildren and his Dallas-based foundation, "Winners for Life," that helps send at-risk kids to college.