The 21-year-old has chosen Barca over their Spanish rivals Real Madrid, after Santos finally allowed their star forward to leave the club.
Many felt that Santos would not permit Neymar to quit South America until after next year's World Cup finals in Brazil.
But he will now join the recently-crowned La Liga champions on a five-year deal at the conclusion of next month's Confederations Cup.
Neymar said: "On Monday I'm signing a contract with Barcelona.
"My family and friends already know about my decision. I want to thank Santos' fans for these nine incredible years. My feelings for the club and the fans will never change."
Santos stressed on Friday they had agreed to transfer Neymar, allowing him to decide between two offers.
The newspaper Folha de Sao Paulo put the latest offer from Barcelona at around $36m.
A Barcelona statement read: "FC Barcelona and Santos have agreed to terms for Neymar da Silva Santos Junior.
"The Brazilian forward will don the Blaugrana strip for the next five seasons. The 21-year old is one of the most promising footballers on the planet."
And Neymar added: "I want to thank the fans of Santos for these incredible nine years. My feeling for the club and the fans will never change. It is eternal!
"Only a club like Santos FC could give me everything I have experienced on and off the field. I thank the wonderful fans who supported me even in the most difficult moments.
"Titles, goals, dribbling, celebrations and songs that fans created for me will be forever in my heart..."