Labor has allocated $125 million in the Queensland budget and QPAC will contribute the remaining $25 million for the 1500-1700-seat theatre. It will be built on the Playhouse Green site.
An international competition will be set up to find the best design for the new theatre,which has been scheduled for completion by 2022.
Ms Palaszczuk said such a large investment in the arts had not been made since the construction of the Gallery of Modern Art,which began in 2004 and was completed in December 2006.
"Brisbane is an important market for touring productions especially major musicals,"she said.
"Queenslanders love live theatre and performance,particularly musicals,and this new theatre will also meet the ever-growing demand to present multiple art forms including theatre,opera,ballet and musicals.
"QPAC is now the busiest theatre complex in Australia ... Building a new theatre is a must to ensure we can keep attracting even more big shows and more visitors to our capital city.
"I have said Queensland Ballet needs a new home,having outgrown the 850-seat Playhouse Theatre,the new larger theatre will enable the company to perform to an audience of double the size within a season."