It marks the 60-year-old's second spell in charge of the national time, having also led them between 2000 and 2002.
Van Gaal takes the reins from Bert van Marwijk, who stepped down last week following Oranje's disappointing Euro 2012 campaign.
"I am pleased the KNVB have approached me," Van Gaal said on www.knvb.com. "This is the challenge I have waited for."
Holland arrived in Poland and Ukraine as one of the favourites for the title having finished runners-up to Spain at the 2010 World Cup in South Africa.
However, they failed to get out of a Group B containing Germany, Denmark and Portugal, losing all three of their matches to finish at the bottom of the table.
Van Marwijk then confirmed his resignation on June 27 following a number of meetings with the KNVB.
The task now falls to Van Gaal, who boasts a wealth of experience in coaching.
During a six-year spell with Ajax, he led them to Champions League success in 1994/95, as well as three league titles, a league cup and the UEFA Cup in 1991/92.
Van Gaal also won two Primera Division titles in charge of Barcelona and coached AZ Alkmaar and Bayern Munich to league triumphs before being sacked by the latter in April 2011 - his last managerial post.
The 60-year-old will be assisted by former Holland defender Danny Blind, and hoping for a more successful time than his first spell in charge of Oranje, when they failed to qualify for the 2002 World Cup finals.
KNVB director Bert van Oostveen is in no doubt Van Gaal is the right man for the job, having beaten off competition from Guus Hiddink, Ruud Gullit and Co Adriaanse.
"We are delighted to be working with each other," he said.
"We looked for a trainer with a wealth of experience and who stood out on both a personal and professional level.
"Van Gaal has a proven track record nationally and internationally and we know him to be a devoted and very passionate coach."
Van Gaal's first match in charge will be the friendly against neighbours Belgium on August 15, before their World Cup qualifying campaign gets under way the following month at home to Turkey.