Wales, under new manager Ryan Giggs, will face Republic of Ireland and Denmark in League B Group Four.
Northern Ireland are in Group Three of League B, and will play Austria and Bosnia-Herzegovina.
Scotland, who are still without a new manager, will play in League C and were drawn into a three-team Group One against Albania and Israel.
Elsewhere, world champions Germany meet France and Holland in League A Group One, while Euro 2016 winners Portugal face Italy and Poland in Group Three of the top division.
The competition’s format will see four leagues of A, B, C and D, split into four groups of three or four teams, which will replace the majority of friendlies and feature promotion and relegation.
The UEFA competition is designed to allow teams to play against those who are similarly ranked - and will offer some who do not qualify for Euro 2020 via the normal route a path to the play-offs.
The Nations League competition will see semi-finals, the final and a third-placed game, held between June 5-9, 2019.
The 16 Nations League group winners will go into play-offs for Euro 2020, to be played in March 2020. If they have already qualified for the European Championship the next best-ranked team in their league will take their place in the play-offs.
Each league has a path of its own, and will consist of two single leg semi-finals and a one-off final.
The winner of each path qualifies for Euro 2020.
At the end of the group stages of the Nations League, those who finish bottom of the groups will be relegated to the league below and four teams will be promoted to the league above.
Wales were in the same World Cup qualifying group as the Republic of Ireland, who then went on to suffer a heavy defeat to Denmark in the play-offs to reach Russia.
Republic of Ireland manager Martin O’Neill is hoping for a better outcome when the countries face off again in the Nations League.
“It (the play-off defeat) is still fresh in the memory so we want to try and avenge that,” said O’Neill.
“There is competition attached to these games, promotion and relegation and it will all affect qualifying for the European Championship so I’m in total agreement with it - once I found out the rules!”
O’Neill has just agreed a new contract to continue in charge of the Republic of Ireland through until 2020.
He added: “I had conversations with the FAI board who wanted me to continue in the job so let’s see how we progress.”
Northern Ireland manager Michael O’Neill is remaining positive ahead of tackling the inaugural UEFA competition.
“I think it’s a good draw. They are two teams that I have not faced yet as an international manager,” said O’Neill, who had turned down the chance to take over as Scotland manager.
O’Neill added: “Austria is a country that we prepared in for the Euros, so it will be nice to go and play there in a competitive game.
“Bosnia again are a strong team, but I think it gives us an opportunity for promotion in the Nations League and also the opportunity to win a place at Euro 2020.”