"One of the extraordinary measures of progress that we've seen in this country has been the recognition that the LGBT community deserves full equality - not just tolerance, but a recognition that they are fully a part of the American family," Obama said.
"I think Americans should be proud that this is just one more step in this ongoing recognition that we treat everybody fairly ... and we judge people on the basis of their character and their performance, not their sexual orientation."
Obama, an avid basketball fan, called Collins on Monday to tell him he supported his decision.
First lady Michelle Obama also tweeted her backing for Collins, who acknowledged that he is gay in Sports Illustrated magazine.
"So proud of you, Jason Collins! This is a huge step forward for our country. We've got your back!" she wrote.