The FA of Iceland said the 51-year-old, who replaced Lars Lagerback in sole charge after Euro 2016, had taken the decision “at his own request”.
Under Hallgrimsson – who continued to work as a dentist while in the job – Iceland drew their first World Cup match against Argentina but were eliminated at the group stage after defeats to Nigeria and Croatia.
Hallgrimsson was initially appointed as Lagerback’s assistant in 2011 but became joint-manager in 2014, helping to mastermind his side’s famous Euro 2016 win over England.
In a statement on Twitter the FA of Iceland said: “[We] can now confirm that Heimir Hallgrimsson will not continue as head coach of the Icelandic men’s national team.
“Hallgrimsson steps down as Iceland coach at his own request after seven years in the job, having joined in 2011.”
Peru World Cup star Paolo Guerrero will be allowed to play for his Brazilian club Flamengo when the Campeonato Brasileiro Serie A resumes this week – despite the fact the striker’s suspension for cocaine use.
In late May, the Swiss Federal Tribunal put a provisional stay on a suspension given to Guerrero by the Lausanne-based Court of Arbitration for Sport (CAS), allowing him to play for Peru in Russia.
It had not been immediately clear if that ruling applied only to the World Cup, raising concern among Flamengo fans that the club might not be able to call upon their veteran star.
But a Switzerland top court said on Tuesday that the May decision “is in force until the court approves other measures or reaches a final decision”.
Guerrero, 34, tested positive for traces of cocaine after a World Cup qualifier between Peru and Argentina on October 5 and was initially banned for a year, which was later reduced to six months on appeal last December.
That ban ended on May 3, making Guerrero eligible to feature for Los Incas at the World Cup.
But instead of accepting the ruling, Guerrero appealed to CAS in a bid to clear his name. Sport’s top arbitration court responded by increasing the reduced six-month ban to 14 months.
The Swiss tribunal could reimpose the suspension after it receives the full argument in support of the decision reached by CAS judges, which is likely to happen by the end of the month.
Olivier Giroud enjoyed silencing his critics after helping France to World Cup glory.
Two decades after helping Les Bleus become world champions as a player, Didier Deschamps led this young, exciting generation to the crown for the second time.
France rode their luck before roaring to a 4-2 victory at the Luzhniki Stadium as Antoine Griezmann and Kylian Mbappe shone in an attack that older head Giroud spearheaded.
The 31-year-old again failed to score as he ended the tournament goalless, leading to criticism that the Chelsea striker quietened by lifting the World Cup.
“Not bad, it’s a great feeling – I mean, ‘it’s coming home!’ I had to say that,” Giroud said with a smile to a group of English reporters.
“Honestly it’s a dream come true, a childhood dream. I am very proud for all the people who supported us, and myself.
“It has been sometimes difficult you know but it is a privilege for me to be part of this team. We have been very solid, very strong all the way, until the end. And I think it’s well deserved.”
Asked to explain what he meant by difficult moments, the striker – proudly wearing his winners’ medal – said: “All of my career I have been, how can I say… I have been through certain difficulties and I have always tried to make it.
“It motivates me to get better and better and go through these difficulties and it is what happens in life when you are really motivated, determined, committed, it is never easy.
“Football is very hard and people see only the nice part of the job. But we work very hard for this achievement and I am very proud to say I am a World Cup champion.”
France boss Deschamps defended Giroud in the build-up to the final, pointing to his diligent work and support play.
That work has been important over the year for club and country, but the striker has come in for flak in his homeland as well as the Premier League.
“No, no, no (I don’t feel more respected in France) because I have been criticised a little but in France as well,” the ex-Arsenal striker said.
“For example, I didn’t score in the World Cup. I receive a lot of messages from people who know football well, lots of French supporters.
“They see the work I do for the team and a lot of people wanted me to score in the final.
“I said ‘yes I hope so but even if I don’t score and we are world champions it will be the best thing that has happened in my life’ so I don’t know if I have had a chance again. I tried to work for the team and I know what I can bring to the team.
“It’s the same for my team-mates. It is not one or two players or 11 players, it is 23 and that was the strength of the French team this year.”
Giroud is glad this French team managed to show everybody what they can do, although he said trying to replicate the “amazing generation” of 1998 did not add extra pressure.
Like then, the triumph was greeted with wild celebrations that is his focus rather than life under new Chelsea boss Maurizio Sarri.
“I need some holidays and after that I will be at Chelsea,” he added.