Apple had removed the apps due to complaints from the Lotteriinspektionen national regulatory body.
The regulator advised Apple that unlicensed operators were targeting players in Sweden.
However, an intervention from the BOS will now enable Apple to reinstate the apps for players in the country to access.
The BOS said it sent Apple a letter explaining that the apps were not in breach of Swedish law as was previously understood by the company.
Gustaf Hoffstedt, secretary general of BOS said: “It is with great satisfaction we can now put this sad history behind us.
“Sweden may not discriminate against foreign companies. It has been confirmed repeatedly by both Swedish law and European Union law.
"Now we can focus on shaping future gaming regulations constructively.
“Together with parliament, the government and the gaming board, we want to promote a non-discriminatory licensing system that treats everyone equally.”