The sneakers will include sketches, lyrics and signatures from Cobain. They are based on trainers worn by the singer and will have wear and fray detailing,
Cobain's widow Courtney Love has sanctioned the promotion, unlike a similar advertising campaign used by Dr Martens.
In a press release, Converse said: "To honour Cobain, in May, Converse will debut their Kurt Cobain collection of shoes featuring artwork and scribbles borrowed from Cobain's personal notebooks.
"It will mark a central part of the year-long 100th Anniversary 'Welcome to the Converse Century' celebration."
Other dead celebrities being used in the campaign include writer Hunter S Thompson, Joy Division's Ian Curtis and Sex Pistols star Sid Vicious.
Kurt Cobain died in 1994 from a gunshot wound to the head.