Speaking in Ankara, Yildirim said: "I thank and express my gratitude to all our citizens who went to the ballot box with a high turnout, and who protected our democracy."
"We have said different things in [rally] squares; we have voiced different things to the nation but the nation gave its final world by saying 'Yes'."
The Turkish premier also said the nation used the ballot box to respond to terror groups.
"In this referendum, our nation gave the best response at the ballot box to the terrorist organization that conducted the July 15 coup attempt, the PKK terrorist organization and foreign powers which treat Turkey as an enemy," he said.
According to Turkey’s government, the Fetullah Terrorist Organization (FETO) and its U.S.-based leader Fetullah Gulen orchestrated the defeated coup of July 2016 which left 249 people martyred and nearly 2,200 injured.
Ankara has also said FETO is behind a long-running campaign to overthrow the state through the infiltration of Turkish institutions, particularly the military, police and judiciary.
More than 1,200 people, including security force personnel and civilians, have also lost their lives since the PKK -- listed as a terrorist organization by Turkey, the U.S. and the EU -- resumed its decades-old armed campaign in July 2015.
'No one lost, the nation is the winner'
Yildirim also congratulated the over 1.2 million young people who went to the ballot box for the first time Sunday.
He added, "There is no one who lost in this referendum, but the winner is Turkey, the winner is the nation."
Saying that Turkey's new government system would be put into practice in the 2019 general elections, Yildirim said: "Our nation made its choice, and it confirmed the presidential system."
He added: "This nation once again demonstrated that it will not bow down to any [military] domination, external intervention, or threat."
Yildirim said that Turkey would protect its unity despite all its differences. "We surely have different opinions and different ideas for solutions, but we will gently protect our unity."
The premier stressed: "Having different opinions never means getting the upper hand over another."
With almost all the ballots counted in Turkey’s historic constitutional referendum Sunday, unofficial results showed Yes won with 51.34 percent -- 24,789,242 votes -- while No had 48.66 percent, or 23,499,390 votes.
Sunday’s referendum asked voters to choose Yes or No on an 18-article bill that would see the country switch from a parliamentary to a presidential system, among other changes.