Putin made the announcement during a press briefing standing beside Hungarian Prime Minister Viktor Orban, following talks in Moscow on Tuesday.
Russian state atomic energy firm Rosatom will build the reactors at the Paks nuclear power plant, which is located about 120 kilometers from the capital Budapest, Presstv Reported.
The landlocked Central European country plans to expand its plant and build two Russian VVER 1200 reactors.
Orban told reporters that they had also agreed on gas supplies for 2020.
The original agreement of building reactors was unveiled in January 2014, just months before the European Union and the United States moved to impose sanctions on Moscow over Crimea's reunification with Russia and Moscow's alleged intervention in eastern Ukraine.
The 28-nation bloc last year gave the final approval for Hungary to expand its Soviet-era nuclear power station using Russian technology and financing.
Brussels has urged EU member states to reduce reliance on Russian energy. Orban has, however, emerged as the most vocal critic of EU sanctions on Moscow.
Amid a flowering of Hungarian-Russian diplomatic ties, Putin has twice been welcomed in Budapest over the past two years.
The Hungarian premier has argued that failing to replace the ageing reactors at Paks would increase Hungary’s dependence on Russian natural gas as an energy source. The plant currently provides around 40 percent of Hungary's electricity needs. The two 1,200-megawatt reactors at the plant will more than double its capacity.