United took Franklin first overall and then grabbed Boswell in the second round.
Franklin spent the last six years with the Los Angeles Galaxy. Named 2008 rookie of the year, he played 160 matches and won two MLS titles with the Galaxy.
He earned US$248,333 this season.
"Sean is in the prime of his career, and we are excited that he is now part of D.C. United," United GM Dave Kasper said in a statement.
Boswell joined D.C. United in 2005 and won Defender of the Year honours in 2006 before leaving for Houston. He played 32 games in 2013 for the Dynamo, making $220,000.
"We are pleased to welcome Bobby back to United,” said Kasper. "Bobby is a seasoned veteran and a winner, and he will provide our back line with solid leadership."
Only Chivas USA gave up more goals (69) than D.C. United's 59 in 2013. United had the league's worst record at 3-24-7.
On Tuesday, United acquired veteran midfielder and captain Davy Arnaud from the Montreal Impact in exchange for an international roster spot for the 2014 and 2015 seasons.
Steve Zakuani, Corben Bone and Marc Burch were the only other players chosen Thursday as most teams elected to wait until the next stage of the re-entry process next Wednesday, allowing them to negotiate new salaries.
Teams that chose players in Stage 1 must either exercise those players' 2014 option or make them a "bona fide offer."
Teams will have seven days to make an offer to the players taken in Stage 2. If an agreement can't be reached, the club will hold the right of first refusal for that player in MLS.
Players not picked up after Stage 2 become available to any MLS club on a first-come, first-served basis.
The Portland Timbers took Steve Zakuani, a former Seattle winger, after trading with Chivas USA to grab the No. 2 selection.
Portland also picked up midfielder-defender Jorge Villafana in the deal while Chivas got the No. 17 selection and defender Andrew Jean-Baptiste.
Zakuani, 25, was the No. 1 overall pick in the 2009 MLS SuperDraft after playing at the University of Akron under current Portland coach Caleb Porter. He earned $233,000 this season.
Bone, formerly of the Chicago Fire, went to the Philadelphia Union while Burch, another Seattle alumnus, was taken by Colorado.
Bone, 25, was taken by the Fire 13th overall in the 2010 draft. He made $49,000 this season.
"We like what Corben can offer to our team going forward,” said Union manager John Hackworth.
Burch, 29, spent the last two seasons with the Sounders, and has 152 regular-season matches under his belt. The defender-midfielder made $75,000 in 2013.
"Marc is a versatile and talented left-sided player with a lot of MLS experience,” said Rapids technical director Paul Bravo.
Toronto's Bobby Convey was one of several players to pull out of the re-entry draft, suggesting another form of move was in the works.
FC Dallas' Kenny Cooper and New England's Kevin Alston also dropped out.
Portland also announced that midfielder Rodney Wallace had undergone successful surgery to repair a torn right anterior cruciate ligament and a non-displaced right tibial plateau fracture as well as a meniscectomy of his right knee.
Wallace, injured in the Western Conference Championship against Real Salt Lake on Nov. 24, is expected to be out five to seven months.
In other MLS news, the Seattle Sounders acquired veteran defender Chad Marshall from the Columbus Crew in exchange for a 2015 third-round pick and allocation money.
Columbus sent its 2014 fourth-round draft pick to the Chicago Fire in exchange for the rights to midfielder Daniel Paladini.
The Houston Dynamo announced the launch of the Houston Dash, a women's pro team that will join the National Women's Soccer League (NWSL) as an expansion team for the 2014 season.
The Dash join the Boston Breakers, Chicago Red Stars, FC Kansas City, Portland Thorns FC, Seattle Reign FC, Sky Blue FC, the Washington Spirit and Western New York Flash.