Boston attended North Fort Myers High School in North Fort Myers, Florida. As a junior, he posted 41 tackles with 16 solo stops, 4 interceptions on defense and caught 43 passes for 736 yards and 5 touchdowns on offense. He was named first-team all-area at defensive back his final two seasons. He was named MVP of the John Carrigan Rotary South All-Star Classic in Ft. Myers in December, 2009. He scored 17 touchdowns as a senior, including 11 rushing, five receiving and one on defense. He led his team with 103 carries for 841 yards, and also had 24 receptions for 364 yards. Defensively, he picked off six passes for 119 yards and recovered one fumble.
Considered a three-star recruit by Rivals.com, he was rated as the 80th best cornerback prospect of his class.
As a true freshman, Boston started 4 games as a cornerback and played in 10 games overall. He finished the season with 32 tackles, four pass breakups, two forced fumbles and one interception. During the Chick-fil-A Kickoff Game against LSU, Boston posted three tackles, forced two fumbles, broke up a pass and made an interception.
As a sophomore, Boston finished the season third on the team with 70 tackles, including 48 primary stops, and led the team with three interceptions for 20 yards. He also broke up 2 passes, recovered 2 fumbles, and forced a fumble. He tied for sixth in the ACC with 3 interceptions. In the Independence Bowl against Missouri, Boston posted 6 tackles.
In his junior season, Boston earned an honorable mention All-ACC honors from both the media and the coaches. He started all 12 games at safety and led the team in tackles with 86 stops on the year, including 49 solo tackles, and added six pass breakups. He also shared the team lead in interceptions with four and returned one for a touchdown. He was also awarded ACC Defensive Back of the Week twice after games against Miami and Virginia. Against Duke, Boston registered a career-high 17 tackles and an interception, including 8 solo tackles. During his senior season, Boston earned second-team All-ACC honors at safety after finishing the regular season with a team-high 85 tackles and four interceptions.
Boston was drafted by the Carolina Panthers in the fourth round (128th overall) in the 2014 NFL Draft.
Boston underwent sports hernia surgery during the offseason on June 4, 2014. Boston earned the starting safety position over Thomas DeCoud midway through the season. He recorded his first career interception and pick six during the final regular season game against Matt Ryan in the win-or-go-home victory against the Atlanta Falcons. For the season, Boston missed just one tackle and allowed just five receptions on 222 coverage snaps, ranking 4th-best among all safeties in the NFL of comparable sample size.
The following week, Boston recorded his first career postseason interception to help clinch a 27-16 Wild Card playoff win for the Carolina Panthers against the Arizona Cardinals.
In the 2015 NFC Championship game, Boston intercepted quarterback Carson Palmer during the fourth quarter of the Carolina Panthers' 49-15 rout of the Arizona Cardinals on January 24, 2016. On February 7, 2016, Boston was part of the Panthers team that played in Super Bowl 50. In the game, he had one tackle but had two penalties as the Panthers fell to the Denver Broncos by a score of 24–10.
In the 2016 season, Boston played in 15 games recording 50 tackles, two interceptions, six passes defensed, and two sacks before being placed on injured reserve with a knee injury on December 27, 2016.
On May 2, 2017, Boston was waived by the Panthers.
On May 15, 2017, Boston signed with the Los Angeles Chargers.