A federal and secular Nepal will have seven provinces, each with its own legislature, according to the new constitution.
President Ram Baran Yadav promulgated the constitution, endorsed by over 90 percent in the Constituent Assembly, at a function in the assembly building.
"The new constitution has institutionalised republicanism in the nation," Yadav said.
Hundreds of thousands of people across Nepal lit lamps to celebrate the event. The government declared a holiday on Monday to mark the occasion.
Security personnel were deployed in the capital Kathmandu to maintain law and order as some parties and groups are opposing the new constitution.
These include the Madheshis, Tharus and a breakaway faction of the UCPN (Maoist).
With the promulgation of the new constitution, there will be fresh election to the top posts like president, vice president, prime minister, speaker and deputy speaker of parliament within a month.
The Constituent Assembly will be dissolved and converted into a regular parliament.
Under the new constitution, the executive rights of the country shall vest with the council of ministers. The president will be a ceremonial head of state.
The preamble of the new constitution says: "Realising a dream cherished by the Nepali people since 65 years, the new constitution will formally take the country towards a federal structure from the existing unitary structure that remained rooted in the country for 240 years."
The new statute has proposed to federate the country into seven units, which will be one of the significant changes.
It also expresses the determination to build an equitable society on the basis of proportional inclusion.
The new preamble refers to multi-party democratic system, civic freedom, fundamental rights, voting rights, press freedom and independent judiciary with a commitment for socialism based on the rule of law.
In 2008, the Maoists won elections to the Constituent Assembly, leading to the abolition of over two centuries of monarchy. But amid squabbling, the assembly failed to draw up a new constitution.