PRESIDENT Tony Tan Keng Yam and Prime Minister Lee Hsien Loong sent their congratulations to King Willem-Alexander on his inauguration on Tuesday as the Netherlands' first king in more than a century.

In a letter sent to Noordeinde Palace, Dr Tan called King Willem-Alexander a "longstanding friend of Singapore" whose ascent to the Dutch throne "comes at a vital juncture in the history of the Netherlands".

"I am confident that under your guiding hand, the Netherlands will continue to flourish and step up to the challenges in an ever changing world." he said.

In his letter, PM Lee expressed confidence that under the new King's reign, "we will take our bilateral relations to greater heights".

"I am confident that you will rule with wisdom and grace," he said.

Both Dr Tan and PM Lee recalled their meetings with King William-Alexander in January this year.

Dr Tan said: "Your Majesty's visit to Singapore in January this year provided an excellent opportunity for us to reaffirm the robust ties between our two nations."

"Singapore and the Netherlands share similar perspectives as small, pragmatic and outward-looking states, and we enjoy strong cooperation in many sectors such as environment and water management, defence, education, culture, and science and technology," he said. "I am confident that we will find new areas of cooperation that will build on our multi-faceted relationship in the years to come."

For his part, PM Lee said King Willem-Alexander's visit led to "a fruitful discussion on many topics of mutual interest".

"Singapore and the Netherlands share similar worldviews and enjoy a longstanding friendship underpinned by wide-ranging cooperation in trade and investment, education, defence, science and technology, and environmental conservation," he said.

King Willem-Alexander became the first Dutch king in more than a century as his mother, Queen Beatrix, abdicated after 33 years as queen.

Dr Tan and PM Lee also sent letters to Queen Beatrix, wishing her well and also recalling her last state visit as a queen to Singapore in January this year.

Dr Tan said: "Your visit to Singapore in January 2013... marked yet another milestone in the already excellent state of relations between our countries. Even as you pass the throne to the able hands of your son, Crown Prince Willem-Alexander, I am confident that you will continue to make important contributions to Dutch society, as you have done through the years."

PM Lee lauded Queen Beatrix's reign in his letter.

"You have inspired many with your generous spirit and commitment to important causes such as peace, tolerance and conservation. Under your leadership, the Dutch monarchy has earned respect for its work ethic, with Noordeinde Palace known as a 'palace of work'. You have represented the Netherlands with dignity, intelligence and empathy," he said.

Visibly emotional, the much-loved Queen Beatrix ended her reign in a nationally televised signing ceremony as thousands of orange-clad people cheered outside. Millions more were expected to watch on television.

The former queen becomes Princess Beatrix, and her son becomes the first Dutch king since Willem III died in 1890.

The 46-year-old king's popular Argentine-born wife became Queen Maxima and their eldest of three daughters, Catharina-Amalia, who attended the ceremony wearing a yellow dress, became Princess of Orange and first in line to the throne.