Speaking in the Scottish Borders, the 89-year-old monarch said the title was "not one to which I have ever aspired".
She has now reigned for 23,227 days - surpassing the reign of her great-great-grandmother Queen Victoria.
Prime Minister David Cameron said the service the Queen had given was "truly humbling".
Dressed in turquoise with her trusty black handbag at her side, the Queen spoke briefly to the gathered crowds earlier.
"Inevitably a long life can pass by many milestones - my own is no exception - but I thank you all and the many others at home and overseas for your touching messages of great kindness," she said.
In the day's main events:
- The Queen and Prince Philip travelled by steam train from Edinburgh to Tweedbank, where she formally opened the new £294m Scottish Borders Railway
- They were accompanied by Scotland's First Minister Nicola Sturgeon, who praised the Queen's "dedication, wisdom and exemplary sense of public service"
- In London, a flotilla of historic vessels, leisure cruisers and passenger boats took part in a procession along the Thames and HMS Belfast sounded a four-gun salute
The exact moment the Queen became the longest-reigning sovereign is unknown. Her father, George VI, passed away in the early hours of 6 February 1952, but his time of death is not known.
Business in the Commons was postponed for half an hour so that MPs, led by Mr Cameron, could pay tribute to the Queen.
The prime minster said she had been a "rock of stability" in an era when so much had changed, and her reign had been the "golden thread running through three post-war generations".
He said it was "typical of the Queen's selfless sense of service" that she thought today should be a normal day.
Acting Labour leader Harriet Harman said it was "no exaggeration" to say the Queen was "admired by billions of people all around the world".
Ministers are to present the Queen with a bound copy of cabinet papers from the meeting in 1952 when Sir Winston Churchill's government approved the content of her first Queen's Speech.
In the House of Lords, leader Baroness Stowell said the Queen had served the country with "unerring grace, dignity and decency", adding: "And long may she continue to do so".
Queen Victoria became queen at the age of 18 and ruled for 63 years, seven months and two days.
Queen Elizabeth's reign has included 12 prime ministers, two more than served under Victoria.
One of those prime ministers, Conservative Sir John Major, rejected any suggestion the Queen had been too passive as head of state: "The monarchy wouldn't be as popular if they were part of politics - they're above and beyond it.
"But when the Queen meets her prime minister she has the opportunity to question, to ask, to counsel. Nobody knows and no prime minister is going to tell you exactly what happens at those meetings. So those who say she's been too passive, how can they possibly know?"