England were drawn by former Portugal striker Nuno Gomes, who scored the winner against them at Euro 2000 to send them out at the group stage
England have avoided Germany in Euro 2020 qualifying but Northern Ireland must face the three-time winners and the Netherlands in Group C.
At 42 in the world, the Czech Republic are the next highest ranked team in England's group, which is completed by Bulgaria, Montenegro and Kosovo.
Germany dropped into pot two for the draw in Dublin after suffering relegation in the Uefa Nations League, and as well as they and the Dutch, Northern Ireland will face Estonia and Belarus.
The Republic of Ireland had initially been drawn in Group C but were handed a reprieve as the group already contained two of the 12 host nations for Euro 2020.
They were therefore placed in Group D instead, along with Switzerland, Denmark, Georgia and Gibraltar.
Fellow hosts Scotland joined Belgium, Russia, Cyprus, Kazakhstan and San Marino, while Wales will meet World Cup finalists Croatia, Slovakia, Hungary and Azerbaijan.
- Euro 2020 qualifying draw: How does it work?
The Euro 2020 qualifiers will take place between March and November 2019, with the winner and runner-up of each group going through directly.
The qualifying process is condensed because of this year's Nations League group games, with England and Scotland guaranteed a Euro 2020 play-off place - should they fail to qualify via their regular qualifying group - after winning their Nations League section.
Wembley will stage both the semi-finals and the final of Euro 2020, as well as three group games and a last-16 match.
Glasgow's Hampden Park and Dublin's Aviva Stadium will each host three group games and a last-16 match.
England had to be placed in a five-team group, as did Portugal, the Netherlands and Switzerland, to ensure they have free dates for the Nations League finals in June 2019.
- Nations League finals draw on Monday: All you need to know
England dealt a kind hand - Analysis
BBC Sport chief football writer Phil McNulty
England and manager Gareth Southgate will make all the traditional - and understandable - cautious noises after the draw but nothing can disguise the fact they have been dealt a kind hand in Dublin.
It is a hand they have helped fashion for themselves with their excellent performances against Spain and Croatia in the Nations League but, realistically, serious questions would be asked if England failed to qualify.
England, currently, are in a different phase of their progress to everyone else in their group and, with Germany avoided, England and Southgate can have no complaints.
Group A: England, Czech Republic, Bulgaria, Montenegro, Kosovo.
Group B: Portugal, Ukraine, Serbia, Lithuania, Luxembourg.
Group C: Netherlands, Germany, Northern Ireland, Estonia, Belarus.
Group D: Switzerland, Denmark, Republic of Ireland, Georgia, Gibraltar.
Group E: Croatia, Wales, Slovakia, Hungary, Azerbaijan.
Group F: Spain, Sweden, Norway, Romania, Faroe Islands, Malta.
Group G: Poland, Austria, Israel, Slovenia, Macedonia, Latvia.
Group H: France, Iceland, Turkey, Albania, Moldova, Andorra.
Group I: Belgium, Russia, Scotland, Cyprus, Kazakhstan, San Marino.
Group J: Italy, Bosnia-Herzegovina, Finland, Greece, Armenia, Liechtenstein.
Source: bbc.com