The draw in Dublin also produced a meeting of host nation Portugal and Switzerland in the last four for the right to reach the final on June 9.
As England were reaching the semi-finals of the World Cup in July, the Dutch had to watch from afar after failing to qualify for a second major tournament in a row.
England won a friendly 1-0 in Koeman's first match in charge in Amsterdam in March, but in his first competitive campaign, the Netherlands beat both world champions France and Germany to a place in the last four of the Nations League.
"We play a team in Holland at a similar stage to us, developing, exciting young players and I can see the impact Ronald has already made with that team," said Southgate, whose side will face the Dutch in the northern Portuguese city of Guimaraes on June 6.
Koeman believes his side's return to form in recent months has restored the pride of Dutch fans in their national team after a lean few years.
"It was difficult the time when we started with the players. We had two big tournaments we didn't qualify for. The best compliment for the players is again the people in Holland are proud of the national team."
The former Everton manager was just as complimentary about Southgate's impact on the Three Lions and in particular his willingness to field young players, something which has traditionally characterised Dutch football.
"We know it's always a battle between England and Holland. We have a lot of respect for the English team and we have a lot of players in the Premier League," said Koeman.
"The way Gareth is managing the English team is how we like (in the Netherlands). He's giving opportunities to young players."
However, there could be disappointment for some travelling fans as the Dom Afonso Henriques stadium in Guimaraes holds just 30,000 with England and the Dutch both expected to bring a strong support.
Will Ronaldo return?
The 50,000-capacity Estadio do Dragao in Porto will host Portugal's meeting with Switzerland on June 5 and the final.
"We are hosting this in our country, with our people, and that brings extra responsibility," said Portugal coach Fernando Santos.
"We have the dream of getting to the final and winning the trophy."
Santos, though, was coy when questioned if Cristiano Ronaldo would return to his side having missed all four Nations League fixtures to date.
With the Champions League final just four days before Portugal's semi-final, Santos hinted that could hinder his preparation and affect any decision on Ronaldo's participation.
"These final games will be decided by the players and it is very close to the Champions League and Europa League finals. It will have an influence on the Nations League and may influence our preparation."
Switzerland shocked Belgium by bouncing back from 2-0 down to beat the number one ranked side in the world 5-2 last month to make the last four.
Vladimir Petkovic's side also beat Portugal in World Cup qualifying two years ago and he is hopeful of pulling off another upset.
"You go to these tournaments to win them," said Petkovic. "We are ready to make a surprise in June."