The decision has been more than 20 years in the making, Ullenhag said, and has been discussed extensively on both parliamentary and international levels.
"I think we should have done it before," Ullenhag told The Local. "But at least we're doing it now."
The suggestion received unanimous support from the governing alliance of Sweden. On Thursday an investigation was launched into how best to implement the decision.
"First, we need to determine if we need something instead of race, a different expression," Ullenhag explained.
He said that in many laws the terminology should be an easy fix - it will still be illegal to discriminate against ethnic background or religion, for instance. The government also needs to make sure the new Swedish law proposals are in line with international human rights conventions.
"There are many international conventions that use the word race, so we have to make sure we don't miss anything. The problem is that the word 'race' is used differently in different countries," Ullenhag said.
Sweden must ensure that the decision complies with the EU Anti-Discrimination Directive, which demands that EU nations provide protection against discrimination on the grounds of "racial or ethnic origin".
But Sweden's step, although seen by some as bold, is hardly ground-breaking. Austria has already "rejected the idea of separate races" and replaced the term race in legal texts
with the term "ethnic affiliation", as is also done in Hungary. In French legislation references are made to "real or assumed" race, another method of watering down the term.
The minister explained that he, along with the Swedish government, desired to scrap the word "race" due to the way the term is used in Sweden - as confirmation that subspecies and "races" of human kind exist.
"The idea of race in Sweden goes back to race biology, and the research we had in Sweden back in the days when we were heavily influenced by Germany," Ullenhag explained.
The Swedish Society for Eugenics (Svenska sällskapet för rashygien) was established in 1909, and in 1922 the Swedish National Institute for Race Biology (Statens institut för rasbiologi) was opened in Uppsala - the first such institution in the world
The research institute was headed for nearly 15 years by Herman Lundborg, a physician with anti-Semitic views and an adamant advocate of "racial hygiene" and eugenics. Some have even said the institute inspired Nazi biopolitics
The Institute later became associated with an sterilization programme for people with "negative" genetic characteristics - a programme which was not terminated until 1975.
In 1999 researchers with the Human Genome Project (HGP) determined that the idea of race has no roots in genetics.
"The concept of race disappeared from scientific discourse more than a decade ago," Juha Kere, Professor of Molecular Genetics at Karolinska Institute, confirmed for The Local on Friday. "It is the broadly accepted conclusion based on worldwide genetic studies that the concept is unfounded."
Professors across the globe have come to the same conclusion, with American anthropologist Loring Brace writing that, while there are genetic differences across the world, there is no visible line
, no clear-cut categories.
"As a rule, the boy marries the girl next door throughout the whole world, but next door goes on without stop from one region to another."
Kere explained that, while there are differences between populations, the genetic variation within each population is greater than the variation between different populations.
"And more importantly," Kere said, "the differences between populations are gradual and reflect the spreading of all humans from Africa. We are all descendants of the early Africans. There are no sharp differences that would in any way reflect the old 'race' definitions."
In other words, the Swedish government decided it's about time.
"It's quite an unmodern term," Ullenhag told The Local. "It implies that we do have different races, and modern science says that we don't."
But while there may be scientific consensus that "race" is indeed an outdated concept, there are those who say that the term still fills a vital function.
The National Afro-Swedish Association (Afrosvensarnas Riksförbund, ASR) has been particularly critical.
"Race may be a social construct, but that doesn't mean it's not a reality," ASR spokesman Kitwamba Sabuni told The Local.
"For us, this is just trying to take away the possibility to even talk about it. It's critical."
Zakarias Zouhir, chairman of the ASR, agreed.
"This path worries me," Zouhir told Sveriges Television
on Thursday. "It's just sweeping it under the blue and yellow rug and pretending there is no racism in society."
Ullenhag responded by saying that the "collective" perspective of the ASR focused on "racification", the claim that "we are all stuck in our races".
"I think that you are on slippery slope there. The problem with that view is that you lose individuality," Ullenhag argued. "I think a liberal way of fighting xenophobia is more effective, where you say that it is always unacceptable to judge people from a collective standpoint. They should always be treated as individual human beings."
Ullenhag stressed that racism and xenophobia will still be hit by legislation even after removing the word race from law. He admitted that, while scrapping the concept of race may not end racism, he believes it is a key "piece of the puzzle".
"We need the political leadership to stand up for the equal value of all humans," Ullenhag told The Local.
"We also need to be crystal clear in Sweden that we will not follow the same path some EU nations have done by following xenophobic forces. Our government has been very clear that, yes, we do have a xenophobic party in parliament, but we will not let them change the political map."