Moreno was born in Seville, Andalusia and came through the youth ranks at Sevilla. He made his first-team debut for Sevilla Atlético on 12 June 2011, in a 3–1 home win over Guadalajara in the Segunda División B play-offs second round second leg (4–5 aggregate).
On 8 April 2012 he made his first-team – and La Liga – debut, coming off the bench for Manu del Moral in the last minutes of a 0–1 away loss against Athletic Bilbao.
Moreno was called up to the senior team on 4 October 2013 for the last 2014 FIFA World Cup qualifier against Georgia, and he made his debut on 15 October, playing the full 90 minutes in a 2–0 win in Albacete.
On 26 August 2014, Moreno made his Liverpool debut in a league match against Manchester City, starting and playing the full 90 minutes in a 1–3 away loss. He scored his first goal for the Reds five days later, netting the last of a 3–0 away win against Tottenham Hotspur, after dispossessing Andros Townsend and sprinting 40 yards to goal in the 60th minute. On 29 December he scored the opening goal against Swansea City in a 4–1 victory for Liverpool at Anfield.
Moreno spent the first four games of the next season as a substitute as new teammate Joe Gomez started in his position. However, on 20 September 2015, he made his first league start of the season, providing the assist for Danny Ings' first Liverpool goal in a 1–1 draw against Norwich City, and was praised for his man of the match performance. His performance in the 2016 UEFA Europa League Final, where Liverpool lost 1–3 to his former club Sevilla, was heavily criticised by pundits and journalists for positioning and defensive errors.
Moreno has many tattoos. In April 2016, he had his leg decorated with an image of a gun-toting chimpanzee dressed in a suit and wearing headphones; ESPN FC's verdict was "Please don't ask, because we haven't got the slightest clue." The back of his leg is decorated with the coordinates of his hometown's Plaza de España. Moreno has two children with his partner Lilia Granadilla.
