Neymar started the 2013 Campeonato Paulista scoring twice in the first match, which ended a 3–1 win over São Bernardo on 19 January 2013. Four days later on 23 January 2013, Neymar scored again against Botafogo in a 3–0 win. On 3 February 2013, in the Paulista fixture against São Paulo, where Santos won 3–1, with Neymar scoring and making two assists. on 18 March 2013, Neymar told that he had a "dream of playing in Europe, for a big club like Barcelona, Real Madrid and Chelsea." But he went on to say, "There's no point in speculating when I'll leave Santos. I'll leave when I want to."
Neymar scored all four goals, had another disallowed and hit the post as Santos beat União Barbarense 4–0 in the Paulista on 13 April. On 25 April 2013, his agent and father revealed that Neymar intended to leave for Europe before the 2014 FIFA World Cup. Ahead of his last match for Santos, on 26 May against Flamengo, Neymar was in tears during the national anthem.
On 24 May 2013, Santos announced that they had received two offers for Neymar. The following day, Neymar announced he would sign with Barcelona on 27 May 2013 and join the team after playing in the 2013 FIFA Confederations Cup. Neither Neymar nor the clubs released details on the transfer fee or personal terms, save to say he signed a five-year deal. On 3 June 2013, Neymar was unveiled by Barcelona after passing medical tests and signing a contract that would keep him at the club through June 2018.
On 30 July 2013, Barcelona drew 2–2 against Lechia Gdańsk in a pre-season friendly; Neymar made his unofficial debut when he came on as a substitute. He scored his first goal for the club in a 7–1 win against a Thailand XI on 7 August. at the Rajamangala National Stadium
On 8 May 2013, Neymar was rated by SportsPro magazine as the most marketable athlete in the world, ahead of Lionel Messi (2nd) and Cristiano Ronaldo (8th). The same month, Neymar launched the Nike Hypervenom football boot. In November 2012 advertising agency Loducca, created Neymar's own personal brand logo, featuring the N, J and R (Neymar Junior) with the N styled to match Neymar's shirt number 11. Neymar starred in a 2014 advert for Beats with other global football stars including Thierry Henry and Luis Suárez, with the theme of 'The Game Before The Game' and the players pre-game ritual of listening to music.
Neymar appeared on the cover of Time magazine in February 2013, the first Brazilian athlete to do so. The issue included an article by Bobby Ghosh entitled "The Next Pelé" and subtitled "How the career of Brazilian football star Neymar explains his country's economy".
In April 2013, Brazilian cartoonist Mauricio de Sousa released a Monica's Gang comic book featuring a younger version of Neymar (called Neymar Jr.) as the main character.
In May 2013, SportsPro magazine named Neymar as the most marketable athlete on the planet for the second consecutive year. He topped the list ahead of Lionel Messi, Rory McIlroy, Usain Bolt and Cristiano Ronaldo, among other sportspeople. The list measures the monetary value, the age, the force in domestic markets, the charisma and their market potential in the next three years. In March 2015, Neymar had the fourth highest social media rank in the world among sportspeople, behind Cristiano Ronaldo, Lionel Messi and David Beckham, with 52 million Facebook fans. He has over 140 million Instagram followers, the third highest for a sportsperson (after Cristiano Ronaldo and Messi), and inside the top 10 most followed people. In ESPN's list of active sportspeople in 2016, Neymar was ranked the fourth most famous athlete in the world. In April 2017, Neymar was included in the Time 100, Time magazine's list of the most influential people in the world. In 2019, ESPN again ranked him the world's fourth most famous athlete.