George was born in Copenhagen, the youngest son of King Frederick III of Denmark and Norway and Sophie Amalie of Brunswick-Lüneburg. His governor from 1661 to 1665 was Otto Grote. He received military training, and undertook a Grand Tour of Europe, spending eight months in 1668–69 in France and mid-1669 in England. His father died in 1670, and George's elder brother, Christian, inherited the Danish throne. In 1674, George was a candidate for the Polish elective throne, for which he was backed by King Louis XIV of France. George's staunch Lutheranism was a barrier to election in Roman Catholic Poland, and John Sobieski was chosen instead.[4] In 1677, he served with distinction with his elder brother Christian in the Battle of Landskrona against Sweden. As a Protestant, George was considered a suitable partner for the niece of King Charles II of England, the Lady Anne. Both Denmark and Britain were Protestant countries, and Louis XIV was keen on an Anglo-Danish alliance to contain the power of the Dutch. Anne's uncle Laurence Hyde, 1st Earl of Rochester, and the English Secretary of State for the Northern Department, Robert Spencer, 2nd Earl of Sunderland, negotiated a marriage treaty.[5] Anne's father, James, Duke of York, consented to the marriage. He was particularly pleased as it diminished the influence of his other son-in-law, Dutch Stadtholder William of Orange, who was naturally unhappy at the match.[6]

In November 1677, Anne's elder sister married a Dutch prince, William of Orange, but Anne could not attend the wedding, as she was confined to her room with smallpox.[14] By the time she recovered, Mary had already left for her new life in the Netherlands. Lady Frances Villiers contracted the disease, and died. Anne's aunt Lady Clarendon (the wife of Henry Hyde, 2nd Earl of Clarendon) was appointed as her new governess.[15] A year later, Anne and her stepmother visited Mary in Holland.[16] Anne's father and stepmother retired to Brussels in March 1679 in the wake of anti-Catholic hysteria fed by the Popish Plot, and Anne visited them from the end of August.[16] In October, they returned to Britain, the Duke and Duchess to Scotland and Anne to England.[17] She visited her father and stepmother in Scotland from July 1681 until May 1682.[18] It was her last journey outside England.[19] Anne's second cousin George of Hanover (her eventual successor) visited London for three months from December 1680, sparking rumours of a potential marriage between them.[20] Historian Edward Gregg dismissed the rumours as ungrounded, as her father was essentially exiled from court, and the Hanoverians planned to marry Prince George to his first cousin Sophia Dorothea of Celle as part of a scheme to unite the Hanoverian inheritance.[21] Other rumours claimed she was courted by Lord Mulgrave (later made Duke of Buckingham), although he denied it. Nevertheless, as a result of the gossip, he was temporarily dismissed from court and despatched to Tangier.[22] On 28 July 1683 in the Chapel Royal, Anne married the Protestant Prince George of Denmark, brother of King Christian V of Denmark (and her second cousin once removed through Frederick II).[23] Though it was an arranged marriage, they were faithful and devoted partners.[24] They were given a set of buildings in the Palace of Whitehall known as the Cockpit as their London residence,[25] and Sarah Churchill became one of Anne's ladies of the bedchamber.[26] To mark their friendship, and at Anne's request, Anne and Sarah called each other the pet names Mrs. Morley and Mrs. Freeman respectively rather than use their formal styles and titles.[27] Within months of the marriage, Anne was pregnant, but the baby was stillborn in May. Anne recovered at the spa town of Tunbridge Wells,[28] and over the next two years, she gave birth to two daughters in quick succession, Mary and Anne Sophia.[29]

His marriage to Anne was arranged in the early 1680s with a view to developing an Anglo-Danish alliance to contain Dutch maritime power. As a result, George was unpopular with his Dutch brother-in-law William of Orange, who was married to Anne's elder sister, Mary. William and Mary became joint monarchs of Britain, with Anne as their heiress presumptive, in 1689 after the "Glorious Revolution" deposed James II and VII, the father of Anne and Mary. William excluded George from active military service, and neither George nor Anne wielded any great influence until after the deaths of William and Mary, when Anne became queen. During his wife's reign, George occasionally used his influence in support of his wife, even when privately disagreeing with her views. He had an easy-going manner and little interest in politics; his appointment as Lord High Admiral in 1702 was largely honorary. Anne's seventeen pregnancies by George resulted in twelve miscarriages or stillbirths, four infant deaths, and a chronically sick son William, who died at the age of eleven. Despite the tragic history of their children, George and Anne's marriage was a strong one. He died aged 55 from a recurring and chronic lung disease, and was buried in Westminster Abbey.

In March and April 1706, George was seriously ill. There was blood in his sputum, but he seemed to recover,[50] although he was too ill to attend a thanksgiving service at St Paul's Cathedral in June for a British victory in the Battle of Ramillies.[51] He missed another thanksgiving service in May 1707, to celebrate the union of England and Scotland, as he was recuperating at Hampton Court.[52] The Scilly naval disaster of 1707, in which a fleet commanded by Sir Cloudesley Shovell foundered, highlighted mismanagement at the Admiralty, for which George was nominally responsible. Pressure grew to replace Admiral Churchill with someone more dynamic.[53] By October 1708, five powerful politicians, known as the Whig Junto—Lords Somers, Halifax, Orford, Wharton and Sunderland—were clamouring for the removal of both Prince George and Churchill. Marlborough wrote to his brother telling him to resign,[54] but Churchill refused, protected by Prince George.[55] Amid the political pressure, George was on his deathbed, suffering from severe asthma and dropsy.[56] He died at 1:30 p.m. on 28 October 1708 at Kensington Palace.[57] The Queen was devastated.[58] James Brydges wrote to General Cadogan, "His death has flung the Queen into an unspeakable grief. She never left him till he was dead, but continued kissing him the very moment his breath went out of his body, and 'twas with a great deal of difficulty my Lady Marlborough prevailed upon her to leave him."[59] Anne wrote, "The loss of such a husband, who loved me so dearly and so devotedly, is too crushing for me to be able to bear it as I ought."[54] Anne was desperate to stay at Kensington with the body of her husband, but under pressure from the Duchess of Marlborough, she reluctantly left Kensington for St James's Palace.[60] Anne resented the Duchess's intrusive actions, which included removing a portrait of George from the Queen's bedchamber and then refusing to return it in the belief that it was natural "to avoid seeing of papers or anything that belonged to one that one loved when they were just dead".[61] Anne and the Duchess had been great friends, but their relationship had become strained over political differences. The immediate aftermath of George's death damaged their relationship further.[62] He was buried privately at midnight on 13 November in Westminster Abbey.[63]