The bill narrowly passed in the upper house of the Dutch parliament, more than a year after MPs passed the legislation.
Pia Dijkstra, who drafted the bill, said under the new system every person over 18 who is not yet registered as a donor will receive a letter asking if they want to donate their organs after death.
The law, which passed 38 to 36, is similar to those in Belgium and Spain.
“They will be able to reply: yes, no, my next of kin will decide or a specific person will decide,” Ms Dijkstra said in a statement.
Those who do not respond to the first letter, or to a second letter six weeks later, will be considered organ donors, although they can amend their status at any time.
The Dutch Kidney Foundation called the vote “a real breakthrough for patients on waiting lists”, saying research in other countries with similar systems shows an increase in registrations of organ donors.
The foundation’s director, Tom Oostrom, said the new law means “hundreds of patients will get back their lives and freedom”.
World news in pictures
The bill will now be signed by Dutch King Willem-Alexander and a minister at the Ministry of Health, Welfare and Sport.
The measure is to come into effect in July 2020 after a publicity campaign.
Associated Press contributed to this report