The American singer was awarded the prize in October but failed to travel to pick up the award, or deliver the lecture that is required to receive the 8m kroner ($900,000;£727,000) prize.
The academy said it would meet Dylan, 75, in private in the Swedish capital, where he is giving two concerts.
He will not lecture in person but is expected to send a taped version.
If he does not deliver a lecture by June, he will have to forfeit the prize money.
A blog entry from Prof Sara Danius, the permanent secretary of the Swedish Academy, said:
"The good news is that the Swedish Academy and Bob Dylan have decided to meet this weekend.
"The Academy will then hand over Dylan's Nobel diploma and the Nobel medal, and congratulate him on the Nobel Prize in Literature.
"The setting will be small and intimate, and no media will be present; only Bob Dylan and members of the Academy will attend, all according to Dylan's wishes."
Prof Darius said taped lectures had been sent by other winners in the past, including Alice Munro in 2013.
Earlier this week, Prof Darius said the academy had had no phone conversations with Dylan and that he had until 10 June to perform the lecture in order to receive the money.
"What he decides to do is his own business," she had said.
In October, Bob Dylan became the first songwriter to win the prestigious award, and the first American since novelist Toni Morrison in 1993.
He received the prize "for having created new poetic expressions within the great American song tradition", the award citation said.
It took him more than two weeks to make any public comment, finally saying the honour had left him "speechless".
He then snubbed the Nobel ceremony in December because of "pre-existing commitments".
But in a speech read out on his behalf, he said he had thought his odds of winning were as likely as him "standing on the moon".
He said it was "truly beyond words" to receive the prize.