The Dutch have been without a head coach since Dick Advocaat stepped down in November after they failed to qualify for the 2018 World Cup finals.
Koeman, who received 78 Netherlands caps in his playing career, had been out of work since he was dismissed by Premier League side Everton back in October.
He has been appointed on a contract that will run until the 2022 World Cup finals in Qatar, which begin in November of that year.
The 54-year-old is Netherlands' fourth head coach since Louis van Gaal left to take over at Manchester United after leading Oranje to third place at the 2014 World Cup.
Guus Hiddink and Danny Blind held the position respectively before Advocaat during a difficult period in which the nation failed to qualify for Euro 2016 or this year's World Cup in Russia.
Koeman's last job at Everton got off to a fine start, as he led the Toffees to a seventh-place Premier League finish and the Europa League group stage.
However, he was unable to repeat that success in the early going of 2017-18 and was sacked in October following a start to the season that saw Everton hovering near the relegation zone.
Previously, Koeman had managed Southampton to a pair of successful seasons after succeeding Mauricio Pochettino, with finishes of seventh and sixth place in the Premier League table.
Koeman was also previously an assistant with the Netherlands national team setup from 1997-98.