They were drawn to play Denmark, Slovenia and Serbia in Group C at the tournament next June, where they will be bidding to finally claim a first major title since the 1966 World Cup.
Third in the latest FIFA world rankings, England are currently seen as the leading contenders to win the Euro along with France, the team that edged them out of last year's World Cup in the quarter-finals.
"We are third in the world rankings this week. We have been in the top five for five years, so consistently they have produced performances, so I think they are used to that," Southgate said of his team, who topped their Euro 2024 qualifying group ahead of Italy without losing a game.
"They have that expectation. They are used to playing in big matches together and individually, so we are excited and all looking forward to the tournament."
Under Southgate, England reached the semi-finals of the 2018 World Cup and lost the final of Euro 2020 on penalties to Italy, before their 2-1 defeat by France in the last eight in Qatar a year ago.
That match was on a knife-edge and could have ended differently had Harry Kane not missed a late penalty.
However, there is confidence that England might now be better equipped to go all the way in Germany next June and July given the current form of Kane at Bayern Munich and Jude Bellingham at Real Madrid in particular.
'Fabulous' Kane
"We are very happy to have those players. We feel that the squad has been building for a long period of time and that England were going to be competitive for the foreseeable future," Southgate said.
"If you are continually in those latter stages, then most teams that win, that is what they do, they go close and they get there."
Kane has scored 22 goals in 18 games in all competitions for Bayern since his move to Germany from Tottenham Hotspur.
"He is a fabulous player," Southgate added.
"The games are a little bit different at the moment at Bayern, because they dominate their games so much.
"He is a very special player, so again he has won so many games for us, not just with his goals which is the obvious factor, but with his link play, his passing ability, the way he leads the line, so we are very fortunate to have him."
England will begin their Euro bid against Serbia, ranked 34th in the world, in the western city of Gelsenkirchen, home to Schalke 04, on June 16.
They will follow that by going to Frankfurt to face Denmark on June 20 in a repeat of the Euro 2020 semi-final which England won 2-1 in extra time.
Their final group game will be in Cologne on June 25 against Slovenia, who England defeated 1-0 at the 2010 World Cup.
"When Denmark came out first you are thinking ok, interesting," Southgate said when it was put to him that England had received a favourable draw.
"Of course everybody was thinking about Italy in one of the lower pots, and Croatia, but I have to say I think Serbia are a very dangerous opponent.
"And Slovenia takes me back to one of my first games as manager really, where but for Joe Hart making one of the best saves I have ever seen, I probably wouldn't be standing here," he added in reference to a 0-0 draw in Ljubljana in a World Cup qualifier in October 2016.
If England top their group, they will play a third-placed team in the last 16 in Gelsenkirchen on June 30.
However, if they finish second they will face the winners of Group A, which contains hosts Germany and also Scotland, in Dortmund.
