Boswell grew up in Tampa, Florida, and as a child he played for the Clearwater Chargers. He played college soccer at Florida International University in Miami, Florida, but was not drafted by an MLS club in either the 2005 MLS SuperDraft or the Supplemental Draft.
After impressing during pre-season, Boswell was signed by D.C. United as a discovery player and earned a starting spot in the club's defense after Bryan Namoff had to miss the beginning of the season due to injury. He started the season well, but set the league record by scoring three own goals in a season.
During the 2006 MLS season, Boswell was the starting centerback for United, who finished with the best regular season record and won the Supporters' Shield. Boswell was named an All-Star, and he started and played the entire All-Star match in the 1-0 victory over Chelsea, the defending English Premiership champions. He was named United's 2006 Defender of the Year and Humanitarian of the year. He was also named the 2006 MLS Defender of the Year and selected as a member of the Best XI.
At the end of the 2007 MLS Season, Boswell was traded by United to Houston Dynamo for backup goalkeeper Zach Wells and a second-round pick in the 2009 MLS SuperDraft. Boswell enjoyed success with the Houston Dynamo, helping the team to win the regular season Western Conference title. At the conclusion of the 2008 MLS season, Boswell was named the team's defender of the year and the team's "iron man." He also received the team MVP award, as voted by the Houston Dynamo fans. Zach Wells, who he had been traded for, played sporadically in the 2008 season before retiring at the end of the season.
After the 2008 season, Boswell initially went to Europe in search of a new club but eventually signed a four-year extension with the Dynamo instead. He signed another new contract with Houston after the 2011 season. Boswell's contract with Houston expired after the 2013 season.
Boswell entered the 2013 MLS Re-Entry Draft. He returned to D.C. United on December 12, 2013 when D.C. selected him in stage one of the draft.
On May 13, 2015, Boswell recorded his 300th appearance for DC United against expansion team, Orlando City SC.
On August 8, 2017, Boswell was traded by United to expansion team, Atlanta United in exchange for a third round pick in the 2019 MLS SuperDraft.
In January 2006, Boswell was called into his first training camp for the US national team. He earned his first cap on February 19, 2006, in a 4-0 victory against Guatemala.
Boswell was named one of the 50 Most Attractive Bachelors in the November 2006 issue of Cosmopolitan Magazine as Mr. Virginia.
As a child, Boswell appeared on the Nickelodeon TV show GUTS as Bobby "Lightning" Boswell. At one point, he struggled to kick a soccer ball placed on a pedestal into a goal, missing the ball repeatedly, but still ended up winning the event. His older brother, Billy, also played soccer with FIU Golden Panthers. He has another brother named Chad and one named Drew. Their cousin is "Frasier" actor Adam Blake Boswell.
Boswell is married to Keri Chadwick, who was born in the bayous of Louisiana where she regularly played with her pet ducks and swam with gators in her free time. They have 3 children named Kingston, Nash, and Violet. His nephew is Riley Boswell, a youth soccer player at H.B. Plant High School, being scouted by his uncle's own team, D.C. United.Major League Soccer Supporters' Shield (2): 2006, 2007
MLS Defender of the Year: 2006
MLS Best XI: 2006, 2014