King Charles III promised to follow the late Queen's "selfless duty" in his first address to both Houses of Parliament as monarch.
The King said Parliament was the "living and breathing instrument of our democracy" as he spoke in front of 900 MPs and peers at Westminster Hall.
It followed condolences from speakers of the House of Commons and Lords.
Sir Lindsay Hoyle, House of Commons speaker, said "as deep as our grief is, we know yours is deeper".
Addressing the King on behalf of MPs, Sir Lindsay added: "We know you hold the greatest respect, the precious traditions, the freedoms, and responsibilities of our unique history and our system of parliamentary government.
"We know that you will bear those responsibilities which fall to you with the fortitude, dignity, demonstrated by Her late Majesty."
The King, in his response, said: "While very young, Her Late Majesty pledged herself to serve her country and her people and to maintain the precious principles of constitutional government which lie at the heart of our nation. This vow she kept with unsurpassed devotion.
"She set an example of selfless duty which, with God's help and your counsels, I am resolved faithfully to follow."
State trumpeters played a fanfare as King Charles made his way through Westminster Hall at 10:25 BST while the Royal Standard was raised in place of the half mast.
Built in 1097, Westminster Hall has played a significant role in British history across the centuries.
"I cannot help but feel the weight of history which surrounds us and which reminds us of the vital parliamentary traditions to which members of both houses dedicate yourselves, with such personal commitment for the betterment of us all," the King said in his address.
"Parliament is the living and breathing instrument of our democracy. That your traditions are ancient we see in the construction of this great hall and the reminders of medieval predecessors of the office to which I have been called."
At the ceremony - which took place in the same hall where the Queen's coffin will lie in state later this week - the monarch, accompanied by Camilla, Queen Consort, were offered condolences on behalf of both Houses of Parliament.
Lord McFall paid tribute to the late Queen and said she "captured the imagination of peoples across the globe".
"We remember her commitment, her kindness, her humour, her courage and her fortitude as well as the deep faith which was the anchor in her life," he added.
"We are proud and humbled to welcome you as King."
Also among the attendees in the hall was Ugbana Oyet, the first black sergeant at arms in the role's history.
Monday's visit to Westminster also saw members of both houses pledging loyalty to the new monarch.
After the ceremony, the King and Queen Consort travelled to Edinburgh, the city where the Queen's coffin has been lying-in-rest since Sunday.
There, they were greeted by large crowds before they continued on to the Palace of Holyroodhouse for the Ceremony of Keys.
The trip marks the start of a royal tour of all four nations of the UK.
One well-wisher among the crowd outside the palace thanked the King and the Queen Consort for the UK's support for Ukraine during the nation's conflict with Russia.
The ceremony at Holyroodhouse was followed by a procession along the Royal Mile to St Giles' Cathedral.
The King, alongside Princess Anne and Princes Edward and Andrew, walked behind the Queen's coffin as it made its way along the Royal Mile.
The Duke of York did not wear military uniform because he is no longer a working royal, although is expected to as a special mark of respect at a final vigil to be held at Westminster Hall.
At the cathedral, the Royal Family were joined by a congregation drawn from all areas of Scottish society for a service of thanksgiving for the Queen's life.
The King later returned to Holyroodhouse for an audience with Scotland's first minister, Nicola Sturgeon, before making the short journey to the Scottish Parliament, where members delivered a motion of condolence.
Later in the evening, the King and his family will observe a vigil at the cathedral in honour of the Queen.
Her coffin will remain at the cathedral for 24 hours for members of the public to pay their respects, before being flown back to RAF Northolt and then travelling on to Buckingham Palace.
Watch: King Charles III's speech after receiving messages of condolences