Britain's royal family, Prime Minister David Cameron and French President Francois Hollande took part in a commemoration at the Thiepval Memorial in northern France to remember the one million who were left dead, injured or missing in the 141-day battle.
Guests from South Africa, New Zealand, Australia, India, Pakistan, Canada and Ireland also attended the event.
Guards of honour, bagpipes and military bands accompanied the moving ceremony in the shadow of the imposing memorial inscribed with the names of 72,000 servicemen who went missing in the surrounding fields.
"The decision has been taken, it cannot be delayed or cancelled," said Hollande, who made a last-minute change to his schedule to attend the ceremony.
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Hollande said a speedy Brexit "would avert all the uncertainties and instability, especially in the economic and financial domains. The faster it goes, the better it will be for them."
"I want to recall that it is the European idea which allowed us to overcome divisions and rivalries between states, and which has brought us peace for the past 70 years," he said in an earlier statement.
"There was high explosives, shrapnel, everything you can imagine. Terrific, hurtling death," read a letter from Private Sean Fendley of the British Army of the first time soldiers went "over the top" to face their German enemy.
The offensive was launched to ease pressure on French forces taking a hammering at Verdun, and was preceded by the largest artillery bombardment in history, with some 1.5 million shells lobbed at the Germans.
The Battle of the Somme was a tragedy not only for British, French and German troops, but also Commonwealth nations whose soldiers fought for Britain.
The commemorations began with the blast of whistles on a former battlefield and in Parliament Square in London at 7:30 am sharp to mark the start of the offensive.
The previous night Queen Elizabeth attended a night-long vigil in Westminster Abbey while her grandson Prince William was in France along with his wife Kate and brother Harry for a vigil at Thiepval.