Gareth Southgate’s men will kick off Group B on the tournament’s opening day against Iran, a side they have never faced in a senior competitive international.
They will also face the United States, who they have met twice in the World Cup finals – in 1950 and 2010 – but never beaten.
England have never faced Scotland or Wales at a World Cup finals, but do have recent European Championship experience against both sides.
Scotland and England played out a goalless draw at Wembley in the group stage of Euro 2020 last June, while Wales and England came together at Euro 2016.
England won that match 2-1 but Wales progressed further in the tournament, reaching the semi-finals.
After opening against Iran, England take on the US before finishing off against their currently unknown European opponents. England boss Southgate dismissed suggestions that uncertainty over one of their Group B opponents could affect preparations for the tournament.
The continued invasion of Ukraine means FIFA is yet to establish a date for their qualifier against Scotland, and the subsequent match against Wales.
Southgate told BBC Sport: “In this situation all our thoughts are with the people of Ukraine, so when this tie is played and how that is played out is irrelevant really.
“It’s for the rest of us to adapt and adjust and provide them with the opportunity to play as and when they are able to.”
England will face Iran on the opening day of the tournament - the first time they have competing on the first day since 1966 - and Southgate added: “We’re in it on day one so it’s quite clear now what our programme looks like from the end of the Premier League season and getting out here as quickly as possible.
“The first two teams (Iran and the USA) we have not played for quite a while and the third is unknown but throws up a possible British derby – and we know what they are all about.”
England captain and striker Harry Kane tweeted after discovering his nation’s fate: “Always exciting to see who we get in the group! Playing on the opening day will be incredible as well.”
One of his predecessors as Three Lions skipper, Alan Shearer, said on BBC Sport: “Gareth will look at that and think it could have been a lot more difficult. He will be happy with that and I’m sure his players will be too.”
Wales caretaker boss Rob Page, meanwhile, said of the potential clash with England on November 29: “It is a mouth-watering tie. Scotland will be thinking the same, but our full focus is on getting there.”
Former Scotland forward James McFadden added on BBC Sport: “It’s a big enough incentive in itself to get to the World Cup, but knowing that you’re going into a group again with England is great and I’m sure it will motivate the players going into those play-off games.”
Hosts Qatar will kick off the tournament against Ecuador on November 21, whilst elsewhere Group E pitted two former world champions Spain and Germany against each other.
Belgium take on fellow 2018 World Cup semi-finalists Croatia in Group F, while reigning champions France take on Denmark, Tunisia and the winner of intercontinental play-off one, which will be one of Australia, the United Arab Emirates and Peru.
If they get through their group, England would face one of hosts Qatar, Holland, Ecuador or Senegal in the last 16.
Group A: Qatar, Ecuador, Netherlands, Senegal.
Group B: England, IR Iran, USA, Scotland/Wales/Ukraine.
Group C: Argentina, Saudi Arabia, Mexico, Poland.
Group D: France, UAE/Australia/Peru, Denmark, Tunisia.
Group E: Spain, Costa Rica/New Zealand, Germany, Japan
Group F: Belgium, Canada, Morocco, Croatia.
Group G: Brazil, Serbia, Switzerland, Cameroon.
Group H: Portugal, Ghana, Uruguay, South Korea.