The ashes, contained in a casket, and accompanied by a piece of broken conch shell, a strip of gold and a copper coin, all contemporaneous, will travel under heavy security and will be placed for a few hours inside the large and splendid Mahabodhi Mahavina Temple, at the site of Buddha's enlightenment.
Their arrival will mark the climax of a four-day ceremony at the temple, which will be attended by India's Prime Minister, Atal Behari Vajpayee.
The relics were discovered by archaeologists in eastern Bihar 40 years ago but have sat in Patna Museum ever since, out of sight. This will thus be the first opportunity for a few of the millions of Buddhist pilgrims who flock to the sacred sites to set eyes on them.
Although Buddhism was born and flourished in India more than 2,000 years ago, Hinduism, with which it shares common roots, supplanted it so thoroughly that today India has new native Buddhists.
But Bodhgaya has been revered for its associations at least since the 7th century, when the Chinese pilgrim Hiuen Tsang visited it.
Today Bihar is one of the poorest and worst-governed places in India. The state's former chief minister, Laloo Prasad Yadav, is in prison, and recently the central government in Delhi tried to impose direct central rule on the state.
Buddhist pilgrims are one of the state's few reliable sources of revenue. The transporting of the relics is perhaps an overdue acknowledgment of their importance.