"Soon, virtually every man, woman and child in America will have access to health insurance they can afford and the vital care they need," Sen. Harry Reid, D-Nev., said in remarks prepared for delivery on the Senate floor.
"Passing the Affordable Care Act was the greatest single step in generations toward ensuring access to affordable, quality healthcare for every American -- regardless of where they live or how much money they make."
Reid said the Supreme Court had "put the rule of law ahead of partisanship."
He said the law would protect Americans against being denied insurance because of a pre-existing condition, among other things.
House Minority Leader Nancy Pelosi, D-Calif., called the high court decision a "victory for the American people."
"With this ruling, Americans will benefit from critical patient protections, lower costs for the middle class, more coverage for families and greater accountability for the insurance industry," Pelosi said in a statement.
She said the law "ensured healthcare would be a right for all, not a privilege for the few. Today, the Supreme Court affirmed our progress and protected that right, securing a future of health and economic security for the middle class and for every American."
House Democratic Whip Steny H. Hoyer, D-Md., urged Republicans to work with Democrats to implement the law.
"Republicans have been trying to repeal the Affordable Care Act since the day it was enacted, and they have been eagerly awaiting today's ruling," Hoyer said in a statement.
"But they must now accept that the Affordable Care Act will remain in place and that the time for litigation and partisan posturing on this issue ought to come to an end. Republicans now have a responsibility to work with Democrats to implement the Affordable Care Act, and I call on them to do so in order to make care affordable and accessible to Americans."
The healthcare law is expected to be an issue not only in the presidential race but in contests throughout the country as Democrats and Republicans vie for control of the House and Senate.
"In one of the most closely followed decisions in its history, the U.S. Supreme Court ruled that President Obama's Affordable Care Act was clearly constitutional," Sen. Dick Durbin, D-Ill., said in a statement.
"This decision means that we can move forward to address the unsustainable increase in healthcare costs and expand the protection of health insurance coverage to over 30 million Americans, including millions in Illinois.
"Those who opposed any change in the law and dismissed the constitutionality of this measure were rejected by the actions of Congress and the opinion of the chief justice."