On 6 March 2019, under the management of Ole Gunnar Solskjær, Greenwood made his competitive debut as an 87th-minute substitute for Ashley Young in a 3–1 win against Paris Saint Germain in the UEFA Champions League. At the age of 17 years and 156 days, he became the second youngest player to represent the club in a European competition (only behind Norman Whiteside) and the youngest ever in the Champions League era. Four days later, he made his Premier League debut from the bench in a 2–0 defeat to Arsenal to become one of the club's youngest league debutants.
On 17 July 2019, Greenwood scored his first senior goal for Manchester United in a 4–0 pre-season victory against Leeds United, and followed it up with a second in United's following friendly against Inter Milan. He began the season making substitute appearances in each of United's first four league matches, before starting their Europa League opener against Kazakhstani side Astana on 19 September; he scored the only goal of the game to become the club's youngest ever goalscorer in European competition at the age of 17 years, 353 days. He then scored a week later in United's League Cup tie against Rochdale. On 29 October, Greenwood scored a late winner for the Manchester United under 21 side in an EFL Trophy match against Doncaster Rovers. On 7 November, Greenwood scored and assisted Martial, in United's 3–0 win over Partizan Belgrade, qualifying them for the knockout stages of the competition. On 24 November, Greenwood scored his first league goal in a 3–3 draw with Sheffield United. On 12 December, Greenwood scored a brace and won a penalty in the final game of the Europa League group stage against AZ Alkmaar. Manchester United won the game 4–0 and finished top of their group. He scored the equalising goal against Everton on 15 December, before scoring his last goal of the decade against Newcastle United 11 days later.
On 30 August 2019, Greenwood was included in the England under-21 squad for the first time and made his debut as a 59th-minute substitute during the 3–2 win against Turkey on 6 September 2019 in qualifying for the 2021 European Under-21 Championship. On 19 November 2019, Greenwood scored his first goal for the U21s; equalising against The Netherlands in a match which England ultimately lost 2–1.
In July 2019, Manchester United manager Ole Gunnar Solskjær praised Greenwood during their pre-season tour, saying: "He can play all of the front-three positions, or across the front four, as he can play number 10, number seven, number 11 and number nine. He's a natural footballer with his left foot, coming in, but he's got two feet and can play anywhere along the front. He's just a natural. When he takes a penalty with his right, then takes a penalty with his left, free-kicks with his left, free-kicks with his right. He is almost what you'd call 50:50, maybe 51:49 left-footed."