The US embassy in Stockholm confirmed the appointment in a statement published on its website.
The US has been without an ambassador to Sweden since the summer of 2015, with the delay in naming a new representative sparking concern among US citizens living in Sweden.
US presidential hopeful Ted Cruz had blocked a Senate vote to confirm President Obama's nominee for the Stockholm post, as well as Obama's nominee for US ambassador to Norway, another appointment which now has approval from the Senate.
Cruz has pledged to block Obama's State Department nominees in protest at the nuclear deal reached between the US and several other world powers, (the P5+1 grouping), and Iran.
According to the New York Times, Cruz staff members, and Senator Mitch McConnell, who had supported Cruz to block nominations, dropped their objections to the ambassadors for Norway and Sweden, as well as several other State Department nominations.
Obama nominated Raji in October 2014.
The previous US ambassador to Sweden, Mark Brzezinski, completed his term on July 1, 2015, since when the role has been filled in a caretaker capacity by Robert Gilchrist, the Chargé D'affaires.