The court, in a 6-3 ruling powered by its conservative majority, upheld a Republican-backed Mississippi law that bans abortion after 15 weeks of pregnancy.
The vote was 5-4 to overturn Roe, with conservative Chief Justice John Roberts saying he would have upheld the Mississippi law without taking the additional step of erasing the Roe precedent altogether.
The decision will intensify debate over the legitimacy of the court, once an unassailable cornerstone of the American democratic system but increasingly under scrutiny for its more aggressively conservative decisions.
The ruling restored the ability of states to ban abortion, with 26 either certain or likely to take that step.
Mississippi is among 13 states with so-called trigger laws to ban abortion with Roe overturned.
In a concurring opinion that raised concerns justices might roll back other rights, conservative Justice Clarence Thomas urged the court to reconsider past rulings protecting the right to contraception, legalising gay marriage, and invalidating state laws banning gay sex.
Justice Brett Kavanaugh appeared to nix an idea advocated by some anti-abortion advocates the next step is for the court to declare the Constitution outlaws abortion.
"The Constitution neither outlaws abortion nor legalises abortion," Kavanaugh wrote.
Biden condemned the ruling as taking an "extreme and dangerous path".
"It's a sad day for the court and for the country," he said.
"The court has done what it has never done before: expressly take away a constitutional right that is so fundamental to so many Americans."
Empowering states to ban abortion makes the US an outlier among developed nations on protecting reproductive rights, the president added.
The president said his administration will protect women's access to medications approved by the US Food and Drug Administration including pills for contraception and medication abortion.
Britain, France and some other nations called the ruling a backwards step, although the Vatican praised it, saying it challenged the world to reflect on life issues.
US companies including Walt Disney, AT&T and Facebook said they will cover employees' expenses if they now have to travel for abortion services.
"The Constitution makes no reference to abortion, and no such right is implicitly protected by any constitutional provision," Justice Samuel Alito wrote in the ruling.
Roe v Wade recognised the right to personal privacy under the Constitution protects a woman's ability to terminate her pregnancy.
"Roe was egregiously wrong from the start. Its reasoning was exceptionally weak, and the decision has had damaging consequences," Alito said.
The court's three liberal justices - Stephen Breyer, Sonia Sotomayor and Elena Kagan - issued a jointly authored dissent.
"Whatever the exact scope of the coming laws, one result of today's decision is certain: the curtailment of women's rights, and of their status as free and equal citizens," they wrote.
The ruling empowered states to ban abortion just a day after the court's conservative majority issued another decision limiting the ability of states to enact gun restrictions.
The abortion and gun rulings illustrate the polarisation in America on a range of issues, also including race and voting rights.
Overturning Roe was long a goal of Christian conservatives and many Republican officeholders, including former president Donald Trump, who as a candidate in 2016 promised to appoint justices to the Supreme Court who would reverse Roe.
During his term he named three to the bench, all of whom joined the majority in the ruling.
Asked in a Fox News interview whether he deserved some credit for the ruling, Trump said: "God made the decision".
Crowds gathered outside the courthouse, surrounded by a tall security fence. Anti-abortion activists erupted in cheers after the ruling, while some abortion rights supporters were in tears.
Hours later, protesters angered by the decision still gathered outside the court, as did crowds in cities from coast to coast including New York, Atlanta, Chicago, Denver, Los Angeles and Seattle.
