He became the country’s first king since 1890 when his 75-year-old mother signed the abdication deed earlier on Tuesday after 33 years on the throne.
Huge crowds of orange-clad partygoers are in Amsterdam to pay tribute.
The queen had announced her intention to stand down in January, saying her son was ready to reign.
Now known as Princess Beatrix, the former queen maintained a recent Dutch tradition of monarch’s handing over power to a new generation.
Willem-Alexander was officially sworn in at a colourful secular ceremony in the Nieuwe Kerk, a decommissioned church, before a joint session of the Dutch parliament.
Crowds in the square outside cheered as the announcement of the inauguration was made from a balcony overlooking the square amid trumpet fanfare.
In the evening, the royal family will take part in a water pageant.
The queen had announced her intention to stand down in January, saying her son was ready to reign and that it was time for the throne to be held by “a new generation”.
She formally relinquished the throne at a short ceremony in the Royal Palace on Tuesday, signing a statement transferring the monarchy to her son “in accordance with the statutes and the constitution of the Kingdom of the Netherlands”.
There were huge cheers from the crowds outside in Dam Square, who were watching the ceremony on giant television screens, as she, her son and his wife Maxima – a 41-year-old Argentine-born investment banker – signed the deed of abdication.
Shortly afterwards, the three royals emerged on a balcony above the square.
The visibly emotional Princess Beatrix told the crowds: “I am happy and grateful to introduce to you your new king, Willem-Alexander.”