The club will also name the new stadium they are building for their B team after the former Dutch international.
Barcelona made the announcement a day after the first anniversary of Cruyff's death at the age of 68.
Cruyff won 13 trophies during his time managing and playing for the club, including their first European Cup in 1992.
His son Jordi also said the family will donate a number nine Barcelona shirt worn by his father and the Ballon d'Or trophy from 1974 to a new Johan Cruyff exhibition at the Spanish club's museum.
"It is an agreement by which my father will always be present at the club that he loved," Jordi Cruyff said.
Barcelona, who are scheduled to start major redevelopment work at the Nou Camp in 2018, will also ask the city's council to name a street or space in the vicinity of their stadium after Johan Cruyff.
"It is an honour for me to say the name of the stadium we are building at the training ground will no longer be the Miniestadi, but from now on will be the Johan Cruyff stadium," club president Josep Maria Bartomeu said.
"Cruyff broke down barriers, he was the man who made us lift our heads up and see that nothing is impossible."
Ajax (as a player): European Cup x 3, European Super Cup x 2, Dutch league title x 8, Dutch Cup x 5, Intercontinental Cup x 1, Super Cup x 1.
Ajax (as a manager): European Cup Winners' Cup x 1, Dutch Cup x 2.
Barcelona (as a player): Spanish league title x 1, Spanish Cup x 1.
Barcelona (as a manager): European Cup x 1, European Cup Winners' Cup x 1, European Super Cup x 1, Spanish league title x 4, Spanish Cup x 1, Spanish Super Cup x 3.
Feyenoord (as a player): Dutch league title x 1, Dutch Cup x 1.
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Barcelona will honour former player and manager Johan Cruyff with a statue of him at their Nou Camp stadium.