The Queen has acknowledged the "difficult and controversial birth" of the new Scottish Parliament building.
The Queen enters the parliament before making her address
She said MSPs must use the world renowned determination of Scottish people to make Holyrood a "landmark of 21st century democracy".
The Queen was speaking during the formal opening ceremony at the new parliament complex in Edinburgh.
The cost was originally estimated at £40m but soared to £431m. The building has been completed three years late.
Saturday's events to mark the opening included a procession down the Royal Mile to Holyrood, followed by speeches in the chamber by the Queen and politicians.
Thousands of people turned out in sunshine to watch the entertainment.
Watch BBC Scotland's programme for the opening of the parliament
The procession, known as the Riding, involved 1,000 people from across Scottish society, travelling down through the historic Old Town to Holyrood.
Each MSP was asked to nominate one person to participate in the Riding from their area who they believed had made a contribution to the lives of other Scottish people either locally or nationally.
The Queen and the main group of dignitaries entered the debating chamber to the sound of Fanfare for the Common Man.
She rose to speak after an address by the Presiding Officer, George Reid, and a haunting unaccompanied psalm sung in Gaelic.
The Queen said she had been moved by watching people from every walk of Scottish life making their way down the Royal Mile.
It was the task of the new parliament to give voice to them, their families and friends.
"Certainly this new parliament building has had a difficult and controversial birth," she said.
The Queen leaves Parliament Hall to go to the Royal Mile
"But that is all the more reason to ensure that with the energy, flair and determination for which Scots are renowned the world over, Holyrood comes to be seen as a landmark of 21st century democracy built securely on the foundations of accessibility, accountability, equality of opportunity and partnership, setting new standards of bringing people and parliament together."
Her speech was followed by performances from the singer-songwriter Eddi Reader and violinist Nicola Benedetti, from West Kilbride, the BBC Young Musician of the Year 2004.
A specially-commissioned poem by Scotland's national poet Edwin Morgan was read by fellow poet Liz Lochhead.
The ceremony ended with Ms Reader singing Auld Lang Syne and in an unscripted addition towards the end, the former Fairground Attraction star asked the audience to join in.
They did so heartily with nearly 500 people singing enthusiastically and holding hands with those next to them.
Even the Queen appeared to sing discreetly although she did not hold hands
with her neighbour George Reid, who was singing at the top of his voice.
But the Duke of Edinburgh sang and held hands with his neighbours on either
side, Mr Reid's deputies Murray Tosh and Trish Godman.
'Good for Scotland'
Before the Riding, First Minister Jack McConnell addressed invited guests in Parliament Hall on the Royal Mile.
"Devolution has been good for Scotland," he told them.
"Scotland has made progress. Far more progress than would have been possible without a Scottish Parliament."
Mr McConnell also referred to the murder of British hostage Ken Bigley in Iraq and said the people of Scotland passed their condolences to his grieving family.
Scottish National Party Holyrood leader Nicola Sturgeon used her short speech in Parliament Hall to call for Scottish independence, drawing applause from some sections of the guests.
Sir Sean Connery and SNP leader Alex Salmond in the Royal Mile
Actor Sir Sean Connery, an SNP supporter, said the whole day had been "exceptional and very moving".
"I was struck by the enthusiasm of crowds greeting the procession and the fact that they represented so many nationalists from across the world all wishing Scotland well," he reflected.
"My highlight was the artists who performed exceptionally. The musicians, Eddi Reader's singing and in particular Liz Lochhead's reading of Edwin Morgan's poem.
"That, I thought, summed up the day of what Scotland should expect from its parliament."
Scottish Tory leader David McLetchie criticised the "astronomical increases in cost and regular postponements" on the building.
He said: "As a patriotic Scot, it is a matter of real regret to me that our parliament has become a source of shame when it should be a source of pride."
Green parliamentary leader Robin Harper said: "In this new building we must inspire, we must connect with our communities and deliver on our promises."
Among the thousands of spectators was Helen Archibald, 64, from Fife, who said: "It's history in the making. I'm just happy to be here."
Presiding Officer George Reid belts out Auld Lang Syne
Her friend, Catherine Bruce, 74, from Edinburgh, said: "I think the atmosphere is wonderful and the parliament looks smashing as well."
Another onlooker, Anne Griffiths, 51, from Musselburgh, East Lothian, said: "Although there has been a lot of controversy about the cost of the parliament, it is going to be part of our heritage so really it is a privilege to be here today."
Meanwhile, Calton Hill played host to a rival party for Scottish republicans organised by the Scottish Socialist Party.