Senators voted 107-13 with seven abstentions on Tuesday to change the constitution, which currently states that marriage is a union between "spouses".
The vote comes after Parliament's Chamber of Deputies last year overwhelmingly approved the same measure.
A senator for the ruling Social Democratic Party, Serban Nicolae, said the vote was on religious grounds, adding: "We've been a Christian nation for 2,000 years."
Social Democrat chairman Liviu Dragnea has indicated Romania will hold a referendum on the issue in October.
Romania, along with Poland, Slovakia, Bulgaria, Lithuania and Latvia, do not recognise same-sex marriage or offer legal protection to same-sex couples.
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