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 ($910,000) prize.
The academy said it would meet Dylan 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 would 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 she had 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.