The relics have been brought to Ireland from Lourdes and will be venerated at churches around the country between now and the start of November.
Born in 1844, Bernadette Soubirous is believed by Catholics to have seen the Virgin Mary 18 times at a grotto in her home town in 1858.
The apparitions were authenticated by the Vatican in 1866 and Lourdes became a place of pilgrimage for people from all over the world.
Bernadette Soubirous died in 1879.
Her body was exhumed for her beatification in 1925 and was found to be uncorrupted, meaning that it showed no signs of decomposition, and was subsequently put on display.
She was canonised in 1933.

St Bernadette has been described as the Virgin Mary’s missionary and today Lourdes is one of the busiest Christian pilgrimage sites in the world, with the Catholic Church acknowledging 70 miracles as having taken place there.
The relic pilgrimage around Ireland is being described as an opportunity for people to have the experience of Lourdes in their own local area.
Organisers say they want the faithful to bear witness, to encourage a spirit of prayer and hope, and to draw on the source of God’s mercy, during their time beside and around the relics.
The tour that starts today in Galway will continue until 5 November, stopping at almost forty different locations.
The relics are on display at the Cathedral of Our Lady and Saint Nicholas today and for much of tomorrow, before they will be brought to Loughrea for the next stage of the tour.
Archbishop Eamon Martin said that the events will be a source of hope, joy and inspiration for people who’ve travelled to Lourdes over the years and for those impacted by illness or disability.
At a special ceremony at the start of the pilgrimage in Lourdes this week, the Bishop of Elphin, Kevin Doran, said the tour would also make it possible for those who could not make it to Lourdes to join in the spiritual benefits associated with the French town.
He said the remains of the saints were a sign of their human condition but that the relics did not have magic powers. Instead, their main purpose was to remind the faithful of the saints and to inspire people to learn from their example.