Born in Seville, Campaña reached Sevilla FC's youth system at the age of seven, and made his senior debuts at only 16, going on to play in two Segunda División B seasons with the reserve team. He was promoted to the main squad by newly appointed coach Marcelino García Toral, for the 2011 pre-season.
On 25 August 2011, Campaña made his debut for the Andalusians' first team, playing ten minutes in a 1–1 home draw against Hannover 96 for the season's UEFA Europa League (2–3 aggregate loss), in the place of Piotr Trochowski. He made his first La Liga appearance three days later, replacing Manu del Moral in a 2–1 home win against Málaga CF.
In his first year, Campaña appeared in 18 official games to help Sevilla to the ninth place. In March 2013, after undergoing surgery to a fracture in his left foot, he was sidelined for the rest of the campaign.
On 13 July 2013, Premier League club Crystal Palace had a €2 million bid accepted by Sevilla. Four days later, after passing his medical, he signed for four years. He made his debut on 24 August, in a 1–2 defeat at Stoke City.
On 31 January 2014, Campaña joined Bundesliga's 1. FC Nürnberg, on loan for the remainder of the season with a view to a permanent move. He made his debut in the competition on 16 February, playing the entire second half in a 1–0 away win over FC Augsburg.
Campaña scored his first goal for the German side on 23 March 2014, but in a 2–5 home loss against Eintracht Frankfurt. He finished the campaign with 591 minutes of action and five starts, with his team being relegated; he subsequently returned to Palace, being one of the retained players.
On 22 July 2014, Campaña joined Serie A side U.C. Sampdoria for an undisclosed fee. However, on 1 September, he was loaned to Portuguese club FC Porto in a season-long deal, becoming the seventh Spaniard brought in by manager Julen Lopetegui in three months.
On 17 July 2015, Campaña signed for AD Alcorcón on loan for one year.
On 11 August 2016, Campaña agreed to a four-year contract with Levante UD, freshly relegated to the second tier.
Campaña represented Spain in two UEFA European Under-19 Championship tournaments. In the 2011 edition, hosted in Romania, he played three games, including the final against the Czech Republic.
In 2012, Campaña helped the national side renew its continental supremacy in Estonia by appearing in all five matches and starting in four, three as captain. He missed, however, his penalty shootout attempt in the semi-finals against France (4–2, 3–3 after 120 minutes).Spain U19
UEFA European Under-19 Championship: 2011, 2012