The defender, who has one cap for his country and previously had a stint in Iran, will link up with the S.League club pending medical and fitness tests
Raspudic, who can play anywhere across the backline and also as a defensive midfielder, received a solitary cap for Bosnia and Herzegovina when he was involved in a 2-2 draw with Poland in December 2010.
With only the formalities of medical and fitness tests to clear, Raspudic will join Croatian defender Robert Alvix, former Ireland international Joseph Gamble and Brazilian Rodrigo Tosi in the Bruneian team's foreign legion.
Raspudic, who scored against Israeli side Maccabi Haifa in the 2011/12 Uefa Champions League qualifiers while playing for Bosnian side FK Borac Banja Luka, wants to help DPMM improve on their eighth-placed finish in 2013.
"I am glad to have signed for a well organised club like DPMM FC," he said in a press statement.
"I see this as a very important milestone in my career. I will do my best to justify the confidence and beliefs of the club management and my representatives, Trebol Sports International.
"My ambition for 2014 is to help the club record better results than last year and hopefully, we can mount a serious challenge for one of the top two spots. I am not very familiar with the other S.League teams but I think we possess a good squad to pose a threat to them.
"This club deserves good results and I am here to ensure that they get them next season."
This will be Raspudic's second foray into Asia, having spent four years with Tractor Sazi Tabriz FC and Petrochimi Tabriz FC in Iran.
DPMM will be led by former Blackburn Rovers manager Steve Kean in the new S.League season, which is expected to start in February 2014.