From Monday, same-sex couples will be able to register to marry, meaning the first ceremonies will take place in February.
Speaking to BBC News NI, Mr McGinn said “everyone who values equality, love and respect can celebrate today”.
“It’s a good day for Northern Ireland, an important day for citizens’ rights across these islands and an exciting day for same-sex couples who can now register to marry,” he said.
Patrick Corrigan from Amnesty International said it was a “historic day for equality and human rights in Northern Ireland”.
“For too long, LGBT+ people in Northern Ireland have been treated as second-class citizens. So, today is an incredible moment for same-sex couples who can finally marry and have their relationships recognised as equal,” he said.