Having started his career at Charlton Athletic, Poyet progress through the club's academy and by May 2013, Poyet signed his first professional contract. Poyet made his professional debut on 21 January 2014 in a 3–0 FA Cup third-round win over Oxford United, entering the match as an 81st-minute substitute for Dale Stephens. He made his first league start for Charlton on 1 February in a 2–1 defeat away to Wigan Athletic. After making these appearance, manager Chris Powell expected Poyet to make more appearances. Despite only becoming a regular in the team in February and playing just 20 league games, Poyet's performances led to him being named Charlton's Player of the Year for the 2013–14 season. On 26 June 2014, Charlton announced that Poyet had indicated that he would not be signing an extension to his contract ending on 1 July 2014, and would be exploring his options elsewhere.
Poyet joined West Ham United on 8 July 2014, signing a four-year contract with West Ham and Charlton reaching a settlement for compensation. His father, Gus, manager of Sunderland, was also keen to sign Poyet, but backed away, citing fear of nepotism which could have caused conflict in the dressing room. On 23 August he made his debut, against Crystal Palace, coming on in the 83rd minute for Mauro Zárate in a 3–1 away win. Four days later he started for the first time, playing the full 120 minutes and scoring in the penalty shoot-out as West Ham lost at home to Sheffield United in the second round of the League Cup. On 7 November 2014, Poyet joined Huddersfield Town of the Championship on a one-month youth loan until 6 December 2014. He was signed by Powell, his former manager at Charlton. The day after he signed, Poyet was an unused substitute as Huddersfield lost 3–1 away at Fulham. He made his début on 22 November at the John Smith's Stadium, playing the full 90 minutes in a goalless draw against Sheffield Wednesday. He played the next game against Bolton Wanderers, but was not included in their 2–1 win over Brentford, and returned to West Ham at the end of his loan.
2015–16 season: loans to Milton Keynes Dons and Charlton Athletic
On 23 July 2015, as a substitute for captain Kevin Nolan, Poyet scored the winner in a penalty shootout at the Ta' Qali National Stadium in Malta, at the end of a 1–1 aggregate draw with Birkirkara in the second qualifying round of the season'sUEFA Europa League. On 19 August, Poyet signed on a season-long loan deal with Championship side Milton Keynes Dons. He made his debut three days later, playing the entirety of a goalless draw away to Reading. His loan spell with MK Dons was cut short in January 2016 by manager Karl Robinson. Poyet had been receiving little playing time due to a similar playing style to team regular and vice-captain, Darren Potter. On 4 January 2016, Poyet returned to Charlton on a loan spell until the end of the season, regaining his old number 39 jersey. Five days later he played the first game of that loan, featuring for the entirety of a 2–1 loss at Colchester United in the FA Cup, and on 12 January he played the first Championship game of the spell, falling 5–0 at Huddersfield. Both of the teams he was loaned to ended the season with relegation to League One.
2016–17 season
Without having played any games for West Ham in the 2016–17 season, Poyet's contract was cancelled by West Ham on 31 August 2016 by mutual consent. He had made 10 appearance in all competitions for West Ham.
Born in Spain to Uruguayan parents, Poyet was raised in England after his father, Gus, signed for Chelsea in 1997. He is eligible to play for any of these three countries. Poyet has represented England at under-16 and under-17 levels and was selected to take part in an England under-19 training camp in May 2014. Poyet received his first call-up to the England under-20 squad for a match with Romania on 5 September 2014, but withdrew from the squad before the game. Head coach Aidy Boothroyd subsequently stated that "Diego hasn't decided whether he wants to play for Uruguay or not so, rather than wait for him to make his mind up, we have decided to leave him to it".
Poyet is the son of Gus Poyet, a former Uruguay international footballer. With his father signed to Real Zaragoza, Poyet was born in Zaragoza in 1995. Poyet's paternal grandfather Washington was a basketball player, who captained the Uruguay national team. His uncle Marcelo also played the sport at a professional level.
