Aloisi was appointed by Brisbane in May and led the club to the final of the Australia Cup, where they lost 3-1 to Sydney FC in October.
He had also overseen a solid start to the new A-League campaign and leaves Brisbane in fifth place in the 12-team competition, six points behind leaders Wellington Phoenix.
"Leaving Brisbane Roar has been a very tough decision for me," Aloisi said in a statement.
"I wholeheartedly believe in the club's progress and direction.
"However, the opportunity presented to me overseas is something that aligns closely with my personal journey and goals as a coach. It's a path I feel I must take at this stage in my career."
Luciano Trani, who had worked as Aloisi's assistant, has been appointed interim head coach for the remainder of the season with Brisbane due to play Melbourne City on Thursday.
