"We are pleased to say that the NC [National Council] elections were a success. We are confident that our switchover to a democratic set-up will be smooth and according to our plans," he said.
The elections were aimed at taking the country from absolute monarchy to constitutional democracy.
Fifteen representatives were elected on Monday but votes in five constituencies were delayed because of a lack of candidates.
Polling in these constituencies will be held on January 29 and King Jigme Khesar Namgyel will nominate five additional members to the 25-member council.
Many of Bhutan’s over 300,000 eligible voters walked for hours from distant villages across the mountain slopes to cast their vote.
And many candidates were in their twenties, partly because the rules required all candidates to be university graduates.
Wangdi said the turnout in Monday's poll was satisfactory but admitted that not everything was smooth sailing.
Several complaints had been made by voters saying they were unable to vote because of bureaucratic glitches.
"Bhutanese people are still not fully aware of the small details of parliamentary elections. But they are soon learning. The response this time was much more than the previous rounds of mock elections [held in April and May last year]," Wangdi said.
The tiny, conservative Himalayan kingdom's transition to democracy began in 2001 when the then king, Jigme Singye Wangchuk, handed over the powers of daily governance to a council of ministers.
In 2006, he abdicated the throne in favour of his Oxford-educated son Namgyel, now 27.
Another round of voting is to take place in February and March, this time to elect the 75-member National Assembly or lower house of parliament, where newly formed political parties can take part.