After graduating from Humble High School in Humble, Texas, Boston became a three-year starter for the Ohio State Buckeyes (1996–98). His 191 pass receptions as a Buckeye remain a team record, as do his career average of 5.2 receptions per game and 910 career punt return yards. His 2,855 receiving yards were a school record until surpassed by Michael Jenkins in 2003. With 36 career touchdown receptions (and one two-point conversion), Boston averaged 5.89 points per game.

Boston's best-remembered moment remains his game-winning five-yard touchdown reception from quarterback Joe Germaine with 19 seconds remaining in the 1997 Rose Bowl.

Boston's father, Byron, is an American football official in the NFL. He was not permitted to officiate regular season games in which David was playing. Byron worked as a line judge for one of his son's preseason games, between the Cardinals and the San Diego Chargers on August 14, 1999.

Boston signed a seven-year, $47 million contract ($12 million guaranteed) with the San Diego Chargers in 2003. That season, he caught 70 passes for 880 yards and seven touchdowns, though head coach Marty Schottenheimer suspended him for a game after he cursed out strength coach Dave Redding. Despite his adequate on-field performance, Chargers GM A.J. Smith traded Boston to the Miami Dolphins for a sixth round draft choice, citing his moody personality and lackadaisical practice habits.

Before the 2004 season, Boston tested positive for steroids and was ordered to serve a four-game suspension. The suspension became academic after he tore ligaments in his knee and was unable to play for the entire season. The Dolphins cut him at the end of the year, then proceeded to re-sign him for the veterans' minimum for 2005. He played in five games that year before tearing knee ligaments again.

On August 23, 2007, Boston was arrested in Pinellas Park, Florida and charged with DUI after a failed sobriety test was conducted. Boston was released on his own recognizance. Boston's breath test resulted in a reading of 0.00 BAC. On September 10, 2007 it was released to the media that David Boston tested positive for GHB, a recreational drug with questionable ties to bodybuilding. After learning of the drug charges the Buccaneers quickly came to an injury settlement with Boston allowing him to be released. On September 12, 2007, Boston was officially released by Tampa Bay when they decided to sign Mark Jones. On December 1, 2011, Boston was accused of beating a woman after a night of drinking in Boca Raton. Boston allegedly punched the woman twice in the head, leaving a gash requiring 10 Stitches, according to a Boca Raton police report. Boston pleaded guilty to a charge of aggravated battery and received a six-month prison sentence. Judge Charles Burton said that he was extending leniency to Boston, turning down the prosecution's request for a term of four years, because of medical evidence that the defendant had incurred permanent brain injuries from the four concussions he sustained during his playing days.

After spending the 2007 season out of football, Boston signed with the Toronto Argonauts of the Canadian Football League on April 21, 2008. Boston reported to training camp but his medical report showed a stress fracture in his right foot and recommended surgery. He was placed on the suspended list, never practicing or playing in the pre-season. A second doctor's opinion, however, was that it was a two-year-old injury and cleared him to play in the regular season opener on June 27, 2008, when he recorded two receptions for a total of 16 yards. Following the game, however, Boston reported feeling too much pain and opted to follow the original doctor's suggestion of surgery requiring a 10 to 12 weeks rehabilitation period. He never played another down of pro football.