England were set to face Cristiano Ronaldo’s Portugal, who knocked them out of successive tournaments in 2004 and 2006, until Traustason’s stoppage-time finish against Austria took his side into second place in Group F, leapfrogging Portugal in the process.
The teams will meet in Nice on Monday.
Iceland are the lowest ranked side left in the tournament, rated 34th in the world by FIFA, and the smallest ever nation to qualify for the European Championship finals with a population of 330,000.
Former Rotherham United midfielder Kari Arnason was man of the match in the 2-1 win over Austria, and admitted he had previously pulled for the Three Lions at major competitions.
“I’ve always supported England in big international tournaments, it’s a dream come true,” said the former Millers midfielder.
“We’re going to go into the game fully focused, we’re going in to get a result. We believe in our ability.”
Arnason, now plying his trade in Sweden with Roy Hodgson’s former club side Malmo, was full of emotion after the final whistle.
It is estimated that around eight per cent of Iceland’s population has made the trip to France, and the 33-year-old lent credence to that claim.
“What we’ve done is fantastic and it’s extra fun to do this beside my best friends,” he said.
“We’re a really tight knit group... and of course all the supporters as well.
“Like I said before it’s like having your family at the game. I know probably 50 per cent of the crowd, or at least recognise them.
“This is extra sweet for us.”
Should England progress the possibility of hosts France in the quarter-finals remains.
While England have a rich history with the Selecao the same cannot be said with Iceland, with only two senior friendlies ever played between the sides.
Their first meeting was a 1-1 draw in Reykjavik in 1982, with England winning 6-1 in their next meeting at the City of Manchester Stadium in 2004.
Current captain Wayne Rooney played in that match, scoring twice, as did assistant manager Gary Neville.
Hodgson showed a certain prescience in the aftermath of England’s goalless draw against Slovakia on Monday, suggesting the slip from first place to runner-up might not be too detrimental in the short term.
“I am disappointed we didn’t top the group, of course, but I am not convinced always that the opponents you will get as a third-placed teams are necessarily going to be easier than one you get as a second-placed team,” he said.
“Let’s wait and see the FIFA ranking of the team we get.”
In that respect, he will allow himself a moment of satisfaction, with Iceland 26 places lower in the FIFA ladder than Portugal’s eighth place.
Joining England, Wales and Northern Ireland in the knockout phase is the Republic of Ireland, after they shocked Group E leaders Italy with a 1-0 win last night.
Former Hull City midfielder Robbie Brady headed the winner to clinch a showdown with hosts France.
His 85th-minute goal saw off Italy at the Stade Pierre Mauroy in Lille to clinch a victory which rekindled memories of the World Cup win over the same opposition at the 1994 World Cup.
Results and tables: Page 22