George Glezmann, who was detained in 2022 while visiting Kabul as a tourist, left Afghanistan aboard a Qatari aircraft on Thursday evening bound for Qatar, the source said.
Glezmann and Boehler are expected to later travel onward to the United States.
US Secretary of State Marco Rubio issued a statement on Thursday confirming Glezmann's release.
Thursday's meeting in Kabul marked the highest-level direct talks between the United States and the Taliban since US President Donald Trump came to power in January.
Boehler met with the Taliban administration's foreign minister Amir Khan Muttaqi, according to a statement by the Afghan foreign ministry.
"During this meeting, discussions were held on Afghanistan-US bilateral relations, the release of prisoners and the provision of consular services to Afghans in the United States," the statement said.
It added that the meeting was also attended by former US special representative to Afghanistan Zalmay Khalilzad.
Qatar, which represents US diplomatic interests in Taliban-ruled Afghanistan, co-ordinated with Boehler to negotiate Glezmann's release with the Taliban authorities, the source said.
"Following weeks of negotiations, a breakthrough was made by the Qataris during recent meetings with the Taliban," the source said, speaking on condition of anonymity.
The Taliban authorities released Glezmann as a "goodwill gesture" and not as part of a deal to free any Afghan detainees held by the US in exchange, the source said.
Glezmann's was the second high-profile release of a US citizen held overseas secured amid diplomacy by Boehler.
Boehler was involved in efforts that led to the release of US school teacher Marc Fogel from Russia last month.
In addition, Boehler has held direct talks with Palestinian militant group Hamas in an effort to secure the release of remaining hostages held in the Gaza Strip.
He also travelled to Iraq last month to push for the release of Israeli-Russian researcher Elizabeth Tsurkov, a student at Princeton University.
Glezmann, a mechanic for Delta Airlines in Atlanta, was visiting Kabul as a tourist when he was detained by the Taliban in December 2022, according to the Foley Foundation, which monitors cases of US citizens detained overseas.
The foundation said Glezmann had been in sporadic telephone contact with his wife since he was detained, and that he had health conditions that deteriorated while in detention.
