The date was decided during a closed-door meeting of cardinals at the Vatican on Monday, the first since the funeral of Pope Francis on Saturday.
The Catholic Church's top dignitaries will retire to the Sistine Chapel in strict seclusion, with all contact to the outside world forbidden.
A two-thirds majority of the 134 cardinals expected to be involved in the conclave is needed to choose Francis' successor in a process that could take days, if not weeks.
The 16th-century Sistine Chapel was closed to tourists on Monday to allow for vote preparations.
The past two conclaves, in 2005 and 2013, lasted just two days. But Swedish Cardinal Anders Arborelius said he expects this conclave may take longer, as many of the cardinals appointed by Pope Francis have never met each other before.
Francis made a priority of appointing cardinals from places that had never had them, such as Myanmar, Haiti, and Rwanda.
"We don't know each other," said Arborelius, one of the cardinals under the age of 80 who will enter the conclave.
Francis died aged 88 on April 21. His funeral on Saturday and a procession through Rome to his burial place at the Basilica of St Mary Major attracted crowds estimated at more than 400,000.
German Cardinal Walter Kasper told La Repubblica newspaper that the outpouring of mourners for Francis indicated that Catholics wanted the next Pope to continue with his reforming style of papacy.
Francis, the first Pope from Latin America, largely tried to open up the often staid church to new conversations. He allowed debate on issues such as ordaining women as clergy and outreach to LGBTQ Catholics.
"The People of God voted with their feet," said Kasper, who is 92 and will not take part in the conclave. "I am convinced that we must go ahead in the footsteps of Francis."
However, a bloc of conservative cardinals are certain to push back against this and seek a Pope who reasserts traditions and restricts Francis' vision of a more inclusive church.
with DPA and AP
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