Rashford, 18, scored within three minutes of his England debut in Friday’s 2-1 friendly win over Australia, having netted eight times in 18 games since making his United debut in February.
His emergence was thought to have cast doubt on Daniel Sturridge’s place, but the Liverpool player was named as one of five strikers despite missing the Australia game with a calf problem.
Originally named in manager Roy Hodgson’s provisional 26-man squad, Leicester City midfielder Drinkwater and Newcastle United winger Townsend made way.
Fabian Delph, the Manchester City midfielder, had previously dropped out of the squad due to a groin problem.
Rashford’s inclusion continues his astonishing rise to prominence and comes a day after he committed his future to United by signing a four-year contract with an option for an extra year.
He only made his United debut, in a Europa League game against Danish side FC Midtjylland, due to injuries to Anthony Martial and Will Keane, but since scoring twice in a 5-1 win, he has not looked back.
He will now look to follow the examples of Michael Owen and Wayne Rooney, who were both teenagers when they announced themselves at major tournaments — the former at the 1998 World Cup, the latter at Euro 2004.
– Drinkwater ‘disappointed’ –
Drinkwater loses out despite playing a key role in Leicester’s stunning 5,000-1 Premier League title triumph.
He had been called up due to fitness concerns over Arsenal midfielder Jack Wilshere and Liverpool captain Jordan Henderson, both of whom have convinced Hodgson that they are ready to make an impact in France.
“Disappointed not to make the final 23!” Drinkwater wrote on his Instagram page.
“Would of been a fantastic experience to go to the euros as a player… But I’ll be supporting the country like I always have! Good luck to the lads… Bring it home.”
Townsend wrote on Twitter: “Obviously gutted to fall at the final hurdle but wishing the boys all the best of luck at Euro 2016.”
The omission of Townsend, who finished the season strongly despite Newcastle’s relegation, leaves England with little recognisable width in attack.
But Hodgson, who will explain his choices when he addresses the media on Wednesday, has stated that his team will use either a 4-4-2 with a midfield diamond or a narrow 4-3-3 system in the tournament.
His side tackle Portugal at Wembley on Thursday in their final warm-up match before travelling to France next week.
England open their Euro 2016 campaign against Russia in Marseille on June 11 and will also face Slovakia and neighbours Wales in Group B.
England 23-man squad for Euro 2016
Goalkeepers: Fraser Forster (Southampton), Joe Hart (Manchester City), Tom Heaton (Burnley)
Defenders: Ryan Bertrand (Southampton), Gary Cahill (Chelsea), Nathaniel Clyne (Liverpool), Danny Rose (Tottenham Hotspur), Chris Smalling (Manchester United), John Stones (Everton), Kyle Walker (Tottenham Hotspur)
Midfielders: Dele Alli (Tottenham Hotspur), Ross Barkley (Everton), Eric Dier (Tottenham Hotspur), Jordan Henderson (Liverpool), Adam Lallana (Liverpool), James Milner (Liverpool), Raheem Sterling (Manchester City), Jack Wilshere (Arsenal)
Forwards: Harry Kane (Tottenham Hotspur), Marcus Rashford (Manchester United), Wayne Rooney (Manchester United, capt), Daniel Sturridge (Liverpool), Jamie Vardy (Leicester City).
Source: London (AFP)