The 1,800 sq metre museum - to be inaugurated in July - will include exhibits on the contributions of Indian civilisation to the world in areas of science, mathematics, medicine, art and language.
It will also chronicle the history and the migration of the Indian diaspora to Canada via Africa, the Caribbean and Fiji.
The aim is to educate the Canadian society, as well as enhance a sense of pride in Indo-Canadians in their heritage, said Naresh Roy Patel, a trustee of the complex.
"The message is one of pluralism - unity in diversity - which will have great importance for all Canadians," he said.
According to the latest Canadian census, there are 713,330 Indo-Canadians in the country or approximately 3 per cent of its total population.
The Indo-Canadian population is mainly concentrated in southern Ontario, Lower Mainland, Calgary-Edmonton Corridor and Montreal.
The museum will be part of the Swaminarayan complex, which includes a Hindu temple and an auditorium, Indo Link, an ethnic newspaper, reported.
Construction of the museum, which began in April 2005, is based on Vedic engineering principles, without using steel or nails, said Naresh Roy Patel, a trustee of the complex.
"It's being done using the same 10,000-year-old traditions, so it's not a replica, it's the real thing. These structures are built to survive for at least 1,000 years," he said.
Slabs of limestone, marble and teakwood were shipped to India where 1,500 sculptors and artisans worked on them and shipped back the finished slabs to Toronto to be assembled by 101 artisans, who were flown in from India.
The cost has been funded entirely through donations, including a gala - Canadian Dollar (C$) 500 per ticket - held at the Swaminarayan complex, raising more than C$250,000.
The first batch of Indians migrated to Canada around the beginning of the 20th century. The pioneers were men, mostly Sikhs from Punjab. Initially, the immigrants faced widespread racism because the Canadians feared that the migrants would threaten their jobs. As a result, there were a series of racial riots that targeted the Sikh immigrants and other Asian groups.
In 1914, a steam liner Komagata Maru carrying 376 passengers from Punjab arrived in Vancouver. Most of the passengers were not allowed to land in Canada and were returned to India. This was one of the most notorious incidents in the history of exclusion laws in Canada designed to keep out immigrants of Asian origin.
According to Statistics Canada, since the late 1990s, roughly 25,000-30,000 Indians have been arriving each year in Canada.