Deputy First Minister Nicola Sturgeon announced the decision as "the right thing to do", saying the government was "committed to a Scotland that is fair and equal".
It intends to publish draft legislation late this year.
The announcement came after nearly 80,000 people took part in a consultation with the government on the issue, which was backed by politicians from all the main Scottish parties.
The consultation recorded 65 percent support for same-sex marriage.
Equality campaigners called the decision "a proud day for Scotland", but the move was quickly slammed by the Catholic Church, which labelled it a "dangerous social experiment".
A spokesman for the Catholic Church in Scotland said: "The Scottish government is embarking on a dangerous social experiment on a massive scale... the church looks much further than the short-term electoral time-scales of politicians."
No religious body will be compelled to perform the ceremonies, the government said.
Tom French, policy co-ordinator for the Equality Network, said: "Same-sex marriage is about equality and freedom: the freedom for couples, and religious and humanist groups that want to, to celebrate same-sex marriages; but equally, upholding the freedom of other religious groups to say no to same-sex marriages."
Jaye and Ruth Richards-Hill, a lesbian Christian couple from Glasgow, said: "We are no longer treated like second-class citizens by our government. We are thrilled that we can now get the religious wedding that we deserve."
A draft bill will now be published later this year.
The UK Government has pledged to legalise gay marriage by 2015 despite opposition from some members of the Conservative party, the biggest party in the coalition government.
The Scottish government, headed by the pro-independence Scottish National Party, has devolved powers from London which allows it to make its own laws on issues including home affairs.