Mirziyoyev replaced Islam Karimov late last year after his death from a stroke following some 27 years of iron-fisted domination over the Central Asian nation.
"This is the first monument to Islam Karimov and a worthy tribute to the first president of Uzbekistan," he said at an event with Turkmen strongman Gurbanguly Berdymukhamedov.
Mirziyoyev, who served as prime minister for 13 years, has shown signs that he might be willing to open up the country's political system, but a transition to democracy seems highly unlikely.
Since he took over, several prominent political prisoners have been released and efforts made to smoothen ties with other countries in the region.
Observers are watching to see if Mirziyoyev moves away from Karimov's foreign policy balancing act that saw strategically located Uzbekistan play Russia, China and the West off against each other.
There was some speculation that Mirziyoyev would make his first trip abroad a symbolic visit to Moscow but instead he opted to head to nearby gas-rich Turkmenistan.
The two leaders also opened two strategic bridges worth almost $500 million connecting the countries with new road and rail links.
The newly built rail link between the two countries is part of a larger link that will extend through Oman, Qatar and Iran.
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