In attendance for the White House ceremony were backers of the bill, Sens. Mazie Hirono, D-Hawaii, Tammy Duckworth, D-Ill., Reps. Judy Chu-Calif., and Grace Meng, D-N.Y.
"My message to all of those who are hurting is: We see you, and the Congress has said, 'we see you,'" Biden said.
"And we are committed to stop the hatred and the bias."
Vice President Kamala Harris also attended the ceremony, noting that she's seen how such hate "can pervade our communities."
"I have seen how hate can impede our progress. And I have seen how people uniting against hate can strengthen our country."
The bill expedites prosecution of hate crimes against Asian Americans and establishes methods to report incidents online. The bill was passed 94-1 in the Senate last month and 364-62 in the House on Tuesday.
The only lawmaker in the Senate to oppose the bill was Sen. Josh Hawley, R-Mo.
Under the legislation, the departments of Justice and Health and Human Services are required to raise awareness of the hate crimes through public outreach. The measure also offers grants to states for creating reporting hotlines.
Stop AAPI Hate, a non-profit that tracks incidents of hate and discrimination against Asian Americans and Pacific Islanders in the United States, said earlier this month it's tracked 6,600 reports of hate incidents since March 2020.
"Those of Asian descent have been blamed and scapegoated for the outbreak of COVID-19 and as a result, Asian Americans have been beaten, slashed, spat on and even set on fire and killed," Meng said when the House passed the bill this month.
"The Asian American community is exhausted from being forced to endure this rise in bigotry and racist attacks."
Harris expressed "outrage and grief" over such hate crimes during a speech Wednesday at the first Asian Americans and Pacific Islanders Victory Alliance unity summit.
She cited the "pain" and "viciousness" of hate crimes targeting the AAPI community during the pandemic, and said the awareness of the moment presents an opportunity for change.