The contentious bill to carve out Telangana from the southern state of Andhra Pradesh was passed by parliament last month amid chaotic scenes in both houses and unprecedented protests by lawmakers.
"The president has signed the Andhra Pradesh Reorganisation Bill. It was the final approval that was required to begin the process of bifurcating the state," Home Ministry spokesman KS Dhatwalia said.
The demand for a separate Telangana state dates back half a century. There has been strong opposition by political representatives from other regions of Andhra Pradesh.
Telangana will comprise 10 of Andhra Pradesh's 23 districts. The remaining region will be known as Seemandhra.
The city of Hyderabad, a major technology hub, would be a shared capital for both states for a period not exceeding 10 years.
Telangana campaigners maintain that their region has been neglected and claim statehood would lead to better administration and faster economic development.
The federal government was keen on pushing the bill through in the current session of parliament, but critics say it was done with an eye on general elections in May.