[4][5] The family moved to Washington, D.C. when Boasberg's father accepted a position in Sargent Shriver's Office of Economic Opportunity, a Great Society agency responsible for implementing and administering many of Lyndon B. Johnson's War on Poverty programs.

[12] In 1996, Boasberg joined the office of the United States Attorney for the District of Columbia where he would spend five and a half years as a prosecutor, specializing in homicides.

[12][11] In September 2002, Boasberg became an associate judge of the Superior Court of the District of Columbia, having been appointed by President George W. Bush.

[15] On February 7, 2014, Chief Justice John G. Roberts announced that he would appoint Boasberg to the United States Foreign Intelligence Surveillance Court for a term starting May 18, 2014 to a seat being vacated by Reggie Walton.

[20] On August 18, 2017, Boasberg dismissed a lawsuit from the Electronic Privacy Information Center (EPIC), which had sued the IRS under FOIA seeking President Donald Trump's personal tax returns from 2010 to the present to be released.

Boasberg concluded that because personal tax returns are confidential, they may only be obtained either by permission from Trump himself or if Congress' joint committee on taxation signed off to allow the disclosure.

[23] In a subsequent decision on July 6, 2020, he vacated an easement to cross the Missouri River pending completion of the environmental review and ordered the pipeline to be emptied within 30 days.

[25] On April 9, 2020, Boasberg issued an opinion finding that the National Marine Fisheries Service violated the Endangered Species Act when it issued a biological opinion in 2014 allowing for the accidental killings of North Atlantic right whales, of which only about 400 remain as of April 8, 2020; by the American lobster fishery, which consists of seven areas spanning the east coast from Maine to North Carolina.