Santos had received offers for Neymar – full name Neymar da Silva Santos Junior – from both Barcelona and its rival Real Madrid, according to Spanish newspaper El Pais, quoting the club's vice-president.
Despite his tender age, Neymar has been a first-team regular for Santos for the past four years, scoring 156 goals and providing 77 assists in 256 matches.
In 2011, he guided them to their first Copa Libertadores triumph since the days when Pele represented the club in the 1960s, and has already established himself at international level, scoring 20 times in 32 appearances with Brazil.
"It's a different moment for me, sad (bidding farewell) and happy (new challenges)," he wrote.
Neymar plays his last game for Santos on Sunday against rivals Flamengo, at the opening of this year's Brazilian football season.
"I want the chance to enter the field one more time... and hear the fans cry out my name," he wrote.