On 31 January 2018, Moura signed a contract with Tottenham Hotspur until 2023 for a transfer fee of around £25 million. He made his debut for Tottenham in the 2017–18 UEFA Champions League match against Juventus on 13 February 2018, coming on as a late substitute in the match that ended in a 2–2 draw. He made his first start as well as scoring his first goal for the club in the FA Cup tie against Rochdale on 18 February 2018 that also finished 2–2.
In the 2018–19 season, Moura scored his first Premier League goal on 18 August 2018 in Spurs' 3–1 win over Fulham. In the following match on 27 August 2018, he scored a brace against Manchester United as Tottenham won 3–0 in only their third away win at Old Trafford in 27 games. He scored his first Champions League goal for Spurs in the group round match against PSV. In the away match against Barcelona at Camp Nou, Moura scored a late equaliser after Barcelona took an early lead in the game. The game ended 1–1, which sent Tottenham through into the knockout stage together with Barcelona. On 13 April 2019, he scored a hat-trick in the 4–0 win over Huddersfield Town. This was his first hat-trick in Europe and the first ever hat-trick scored at the new Tottenham Hotspur Stadium.