In a speech at the monument where France's most respected sons are buried, along with just four of its daughters, Macron said honouring Veil was a "decision of all the French people".
"With Simone Veil, those generations of women who have made France without the nation offering the recognition or the liberty that was their due enter here," the president, who was accompanied by his wife, Brigitte, declared.
Veil, whose death a year ago, sparked an outpouring of emotion, was taken to Auschwitz-Birkenau concentration camp along with her family in 1944 at the age of 16.
Her mother, father and brother died in the Holocaust.
She went on to become health minister and introduce limited abortion rights for women in 1974, becoming the first elected president of the European parliament in 1979.
Passion for Europe
On Sunday, as thousands watched, her flag-draped coffin and that of her husband, Antoine, were taken into the crypt of the Panthéon to the strains of Bach's fifth cello suite.
They had been carried along a blue carpet, the colour chosen to symbolise her enthusiasm for the European Union.
"We owe it to Simone Veil not to allow the doubts and the crises that are assailing Europe attenuate the stunning victory that for the last 70 years we have won over the traumas and mistakes of past centuries," Macron said.
The coffins will lie in state until Monday and admission to the monument will be free of charge from 1-8 July.
Silence of concentration camp
They had been on show at Paris's Museum of the Shoah for 48 hours.
A minute's almost-silence, recorded at Auschwitz a few days ago, was played after Macron's speech, followed by a rendition of the Marseillaise by opera singer Barbara Hendricks.
The year's gap between Veil's death and her transfer to the Panthéon was much shorter than that observed for the 72 men and four women who preceded her.
Veil's husband, Antoine, a senior civil servant who went into business, died in 2013.