Yesterday, the 'Yes' side won 51.41 percent of the vote compared with 48.59 for the 'No', near full results showed.
The lira was trading at 3.67 against the US dollar at 0800 GMT, its value jumping by 1.6 per cent.
Since the start of this year, the lira has lost four percent of its value against the greenback because of political instability making it the worst-performing emerging market currency in 2017.
The Istanbul stock exchange also rallied after the result, up by 0.74 per cent immediately after market opened. By 0800 GMT, stocks had risen by 0.6 per cent.
"The market is likely to cheer the continuation of stability, declining chances of an early election and the tight call on the referendum that may contain any market- unfriendly moves," Ozgur Altug, chief economist at Istanbul- based BGC Partners, said.
But Altug said that despite the welcome from the market in the near term, "we do not expect a major breakout".
Turkey remains under a state of emergency introduced after last year's failed coup, expected to be extended by the government for another three months.
And in the last 18 months, the country has been hit by a slew of terror attacks blamed on Kurdish militants and jihadists, killing hundreds.
Turkish voters have approved an executive presidency that will see more power in the hands of Erdogan with the role of premier axed and "one or more" vice presidents chosen by the head of state.
Unemployment figures released on Monday showed a rise in January jobless to 13 per cent, a 1.9 percentage point increase compared with the same period in 2016, the Turkish statistics office said.
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