But Ban stressed that more should be done in Uganda to decriminalize same-sex relationships and fight discrimination against lesbians, gays and transgender persons.
The top court nullified legislation signed by long-serving President Yoweri Museveni that made homosexuality a crime punishable by life in prison, citing a lack of quorum of lawmakers for its adoption.
Ban paid tribute to "all those who contributed to this step forward, particularly the human rights defenders in Uganda who spoke out, at times incurring great personal risk," a statement from his spokesman said.
Homophobia is widespread in Uganda, where American-style evangelical Christianity is on the rise.
Gay men and women face frequent harassment and threats of violence.
The law is "null and void", presiding judge Steven Kavuma told the court on Friday, saying the process had contravened the constitution, as it has been passed in parliament in December without the necessary quorum of MPs.
Cheering gay rights activists celebrated the ruling, but supporters of the law said they would appeal at the Supreme Court.
"Justice prevailed, we won," said lawyer Nicholas Opiyo, who led the challenge in the constitutional court.
"The retrogressive anti-homosexuality act of Uganda has been struck down by the constitutional court - it's now dead as a door nail," said Andrew Mwenda, one of 10 petitioners.
The law, signed by Uganda's veteran President Yoweri Museveni in February, said that homosexuals should be jailed for life, outlawed the promotion of homosexuality and obliged Ugandans to denounce gays to the authorities.
US Secretary of State John Kerry likened the law to anti-Semitic legislation in Nazi Germany, and Western nations made a raft of aid cuts to Uganda's government.
But homosexuality in Uganda remains illegal and punishable by jail sentences under previous legislation, which is expected to return after the court's decision.
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