Gujarat Governor OP Kohli, Chief Minister Vijay Rupani and BJP chief Amit Shah were present at the unveiling of the 'Statue of Unity'.
The ceremony coincided with Patel's 143rd birth anniversary.
Had Sardar Patel not united the country, we would need visas to see lions or pay homage at Somnath or view the Charminar in Hyderabad, the prime minister said.
He added that the statue will remind those who question India's existence that this nation was, is and will remain eternal.
He described the Statue of Unity as a symbol of the country's engineering and technical capabilities.
The imposing monument is twice the height of the Statue of Liberty in the US and is built on an islet, Sadhu Bet, near the Sardar Sarovar Dam in Gujarat's Narmada district.
It has been built using over 70,000 tonnes of cement, 18,500 tonnes of reinforcement steel, 6,000 tonnes of structural steel and 1,700 metric tonnes of bronze, which was used for the outer cladding of the structure.
A viewing gallery has been created at a height of 135 metres inside the statue to enable tourists to have a view of the dam and nearby mountain ranges.