The 71-year-old, who has battled with cancer over the last year, concluded his third spell as the Netherlands coach with their penalty shootout loss and will be replaced by Ronald Koeman.
"In principle this is it for me," said Van Gaal earlier in the tournament, "but you can never say never".
He had been brought out of retirement when Frank de Boer was fired after elimination in the last 16 of the European Championship by the Czech Republic for a third spell in charge of the Dutch.
Van Gaal took over in September last year, leading the Dutch to World Cup qualification, after they had missed out on the 2018 finals in Russia.
They also won their Nations League group and will host the finals in June against Croatia, Italy and Spain.
Van Gaal had also been coach when the Dutch reached the 2014 World Cup finals, beaten then also on post-match penalties by Argentina.
That proved the high point of a career that included Champions League success with Ajax Amsterdam, two LaLiga titles at Barcelona, the Bundesliga with Bayern Munich but a disappointing spell at Manchester United, although they did win the FA Cup in 2016.
All of which was characterised by a reputation for meticulous planning and attention to detail but also a single-minded belief in his own ability that won him many admirers and detractors in equal measure.
His battles with the media were many, spawning even a book by one reporter about his many encounters with Van Gaal.
The coach revealed in April he had received 25 radiation treatments for an aggressive form of prostate cancer, having kept the diagnosis from his players during the World Cup qualifiers.
They had been unaware Van Gaal was wearing a catheter beneath his tracksuit during training sessions or that he was spending nights after matches in hospital.
He has also said any future jobs would depend on the agreement of his wife Truus, who he had twice promised before that he would go into retirement only to reverse his decision.
Koeman (59) will take over, having already signed in April a three-year deal to return as Netherlands boss from 2023.
It will be Koeman's second spell in charge of his country, having led them to runners-up in the Nations League in 2019 and qualification for Euro 2020 before ditching the job when Barcelona offered him a chance to coach them in August 2020. He lasted only 14 months before being fired by the Catalan club.
"I am looking forward to the new collaboration. I certainly did not leave the Dutch national team out of dissatisfaction," Koeman said when he signed the contract.
"My stay felt good, the results were good and the click with the internationals was good. We will soon continue on that path. That is certain for me."
