At a meeting for the United Nations High Commissioner for Refugees (UNHCR) in Geneva, the displacement of Syrian refugees has been high on the agenda.
The Swedish delegation has been leading an international working group with the task of finding homes for an estimated 34,000 Syrian asylum seekers, Sveriges Radio reports.
Following talks between Billström and dozens of other senior politicians, a total of 21 countries around the world have agreed to follow Sweden's lead in tackling the issue.
Billström said the agreement would enable the Syrian asylum seekers to seek refuge in a safe zone, most likely in the EU.
"It feels very good and fortunate that this is happening," he told Sveriges Radio.
In September last year, Sweden granted permanent residence to all Syrian refugees who applied, the first country in the EU to do so.
Earlier in June it was revealed that Sweden took in almost 20 percent of EU's asylum seekers, more than any other nation – despite only representing 1.9 percent of the EU's population.
In 2013 Sweden took in 26,395 asylum seekers, of which Syrians made up 46 percent.
By contrast, Germany took in 26,080 refugees (12,000 Syrians), while certain other countries in the EU, such as Austria, took in significantly smaller numbers of Syrians than Sweden.
That looks set to change following the agreement with the UNHCR, as Austria has agreed to take in 1,500 Syrians over the next year. Sweden is expected to rehouse another 1,200 Syrians.
Billström praised Germany for promising to provide asylum to 20,000 more people as part the agreement.
However, he said he was "especially disappointed" that just 14 of the EU's 28 member states were stepping up and participating in the refugee rehousing scheme.
In 2013, Sweden was UNHCR’s fifth largest donor. Sweden remains one of the non-profit organization's top partners, contributing 768.5 million kronor ($117.2 million) so far this year.