The Commonwealth Heads of Government Meeting (Chogm), held every two years, will focus on climate change, with talks on security issues also expected.
UK Prime Minister David Cameron has pledged to set up a Commonwealth unit to target the "scourge" of extremism.
The group of nations has a vital role to play in tackling terrorism, he said, and pledged Â£5m to help fund the unit.
Security was high around the Queen as she arrived with the Duke of Edinburgh, the Prince of Wales and Duchess of Cornwall.
Opening the conference, the Queen said she was enormously proud of what the Commonwealth had achieved and "all of it within my lifetime".
She said Commonwealth nations would continue to be called on to demonstrate leadership in global issues.
Counter-terrorism is top of Mr Cameron's agenda for the meeting in the Maltese capital, Valletta.
It comes after he addressed MPs in the UK to state his case for military air strikes in Syria to tackle so-called Islamic State.
Mr Cameron said of the Commonwealth unit: "The Commonwealth has a vital role to play in broadening international efforts to counter extremism.
"Its civil society and education networks make it particularly well placed to complement international efforts to build counter narratives to this poisonous extremist ideology.
"This is the struggle of our generation, but by working together we will defeat this extremism scourge that is a threat to us all."
Mr Cameron has pledged Â£1m funding annually, for five years, to help set up the unit, with another Â£200,000 going on expanding a European counter-radicalisation youth programme to include the Commonwealth.
French President Francois Hollande is due to arrive in Malta on Friday and will attend meetings on climate change ahead of a summit on the issue in Paris on Monday.
By Nicholas Witchell, royal correspondent, BBC News
It is an association of 53 independent nations, disparaged sometimes as little more than a talking shop, but between them the countries of the Commonwealth represent nearly one-third of the world's population.
As its heads of government gather in Malta, there are pressing matters to consider.
Countering violent extremism is a priority; so too is climate change, the effects of which are a particular threat to low-lying territories in the Pacific.
And a few days short of the Paris conference on global warming, French President Francois Hollande is breaking off from his domestic security challenges to address Commonwealth leaders on the need for decisive action on global warming.
The conference will be formally opened by the Queen in her capacity as Head of the Commonwealth: no-one has been to more of these gatherings than she has but, since by the time of the next meeting she'll be 91, it is thought this might be the last Commonwealth conference she'll attend.
The Queen will later host a reception for new Commonwealth leaders.
The event will feature more than 360 artists and performers, including the Maltese Philharmonic Orchestra and tenor Joseph Calleja.
The Royals are on a three-day tour of Malta, where the Queen and the Duke of Edinburgh lived at the start of their marriage in 1949, the same year the Commonwealth was founded.
In her opening address, the Queen paid tribute to her husband for his "boundless energy and commitment".
"For more than six decades of being head of the Commonwealth, a responsibility I have cherished, I have had the fortune of the constancy of the Duke of Edinburgh," she said.
She also has thanked her son, the Prince of Wales, for his support and "great distinction".

The 29-year-old spent the latter half of last season on loan at McDiarmid Park from Coventry City.
He signed for Hearts after being released by the English League One outfit but made only nine appearances for Saints' Premiership rivals.
The former Berwick Rangers, Dundee United and Peterborough United winger has signed an 18-month contract.
Swanson had been released by Hearts on Monday and was signed by Saints as a replacement for Michael O'Halloran, who had been sold to Rangers the same day.
He made 12 appearances in his previous spell with the Perth club, scoring twice.
The Queen has opened a two-day summit of leaders of the 53 Commonwealth nations in Malta.
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Winger Danny Swanson has returned to St Johnstone after a frustrating five months with Hearts.