Joe Biden will be a "true friend of Ireland", Taoiseach Micheál Martin has said, as he celebrated the new US President's ancestral links to the country.
"Today a true friend of Ireland, Joe Biden, became the 46th President of the USA," Mr Martin said on Twitter.
"It is a day of history and hope and I look forward to forging ever closer ties between our two great nations."
Mr Martin also paid tribute to Vice President Kamala Harris, saying she had created history and "will help form a diverse and formidable administration".
Ms Harris is the first woman to become vice-president, as well as the first black person and the first person of South Asian descent to serve in the role.
President Michael D Higgins has offered his "heartfelt congratulations" to Mr Biden.
In a letter to President Biden, President Higgins said: "There can be no greater honour than to be given the trust of one's fellow citizens to lead."
"There can be no greater honour than to be given the trust of one's fellow citizens to lead."— President of Ireland (@PresidentIRL) January 20, 2021
President Michael D. Higgins has written to President Joe Biden, offering his "heartfelt congratulations" as @JoeBiden assumes the office of President of the United States. pic.twitter.com/grdf6hBVYN
In a statement, Mr Martin added: "I know that President Biden will feel the weight of history, the presence of his Irish ancestors who left Mayo and Louth in famine times in search of life and hope.
"He will remember their descendants' hard struggle as they made their way in and their contribution to the United States. It is the story of Irish-America.
"I hope he will also be conscious of the great pride we in Ireland take in his immense achievement. He is one of us, part of our global family.
"I look forward to welcoming President Biden back to this island and deepening cooperation on global peace, climate change, economic partnership and stability."
Other world leaders have also offered their congratulations to the new president and his administration.
British Prime Minister Boris Johnson said he was looking forward to working with the Democratic successor to Donald Trump.
Mr Johnson said America's leadership is "vital" to the rest of the world, from tackling the climate crisis to the coronavirus pandemic, as Mr Biden took the oath of office during a ceremony at the US Capitol.
Congratulations to @JoeBiden on being sworn in as President of the United States and to @KamalaHarris on her historic inauguration. America's leadership is vital on the issues that matter to us all, from climate change to COVID, and I look forward to working with President Biden.— Boris Johnson (@BorisJohnson) January 20, 2021
Israeli Prime Minister Benjamin Netanyahu has urged Mr Biden to "strengthen" a long-standing alliance between the two countries, partly in order to confront the "threat" posed by Iran.
"I look forward to working with you to further strengthen the US-Israel alliance, to continue expanding peace between Israel and the Arab world and to confront common challenges, chief among them the threat posed by Iran," he said.
Iranian President Hassan Rouhani hailed the departure of "tyrant" Mr Trump, Tehran having repeatedly called on Washington to lift sanctions imposed over its nuclear drive.
"We expect (the Biden administration) to return to law and to commitments, and try in the next four years, if they can, to remove the stains of the past four years," said Mr Rouhani.
Mr Biden's administration wants the US back in the landmark Iran nuclear accord, from which Mr Trump withdrew, provided Tehran returns to strict compliance.
Canadian Prime Minister Justin Trudeau said he looked forward to working with the new president to fight Covid-19 and climate change.
In a statement, Mr Trudeau said the two countries "will continue this partnership as we fight the global Covid-19 pandemic and support a sustainable economic recovery that will build back better for everyone".
"We will also work together to advance climate action and clean economic growth, promote inclusion and diversity, and create good middle class jobs and opportunities for our people while contributing to democracy, peace, and security at home and around the world," Mr Trudeau said.
There is no time to waste when it comes to tackling the crises we face. That's why today, I am heading to the Oval Office to get right to work delivering bold action and immediate relief for American families.— President Biden (@POTUS) January 20, 2021
European Commission President Ursula von der Leyen has said she looked forward to having a friend in the White House.
She said she hoped Mr Biden could work with Europe on fighting climate change, quashing the Covid-19 pandemic and rebuilding multilateralism.
Meanwhile, Russia has urged President Biden's new administration to take a "more constructive" approach in talks over the extension of the New START treaty, Washington's last arms reduction pact with Moscow.
"We expect that the new US administration will take a more constructive approach in its dialogue with us," the Russian foreign ministry said in a statement.
"We are ready for such work on principles of equal rights and taking mutual interests into account."
To @JoeBiden and @KamalaHarris.— Emmanuel Macron (@EmmanuelMacron) January 20, 2021
Best wishes on this most significant day for the American people!
We are together.
We will be stronger to face the challenges of our time. Stronger to build our future. Stronger to protect our planet. Welcome back to the Paris Agreement!
Pope Francis told President Biden that he was praying that God would guide his efforts to bring reconciliation in the United States and among the nations of the world.
In a message sent shortly after the second Catholic US president was sworn in, Francis also said he hoped Mr Biden would work towards a society marked by true justice, freedom and respect for the rights and dignity of every person, especially the poor, the vulnerable and those with no voice.
"The bond between North America and Europe is the bedrock of our security, and a strong NATO is good for both North America and Europe," said NATO General Secretary Jens Stoltenberg.
"NATO Allies need to stand together to address the security consequences of the rise of China, the threat of terrorism, including in Afghanistan and Iraq, and a more assertive Russia."
German President Frank-Walter Steinmeier said he was "greatly relieved" Mr Biden was replacing Mr Trump as US President, calling it a "good day for democracy".
Germany looked forward "to knowing we again have the US at our side as an indispensable partner" in addressing "the coronavirus pandemic, climate change, security issues, arms control and disarmament, and many urgent conflicts around the world".