Three gay men say they have gained legal recognition as the first "polyamorous family" in Colombia, where same-sex marriages were legalised last year.

"We wanted to validate our household... and our rights, because we had no solid legal basis establishing us as a family," said one of the men, actor Victor Hugo Prada, in a video published by Colombian media on Monday.

He said he and his two partners, sports instructor John Alejandro Rodriguez and journalist Manuel Jose Bermudez, signed legal papers with a solicitor in the city of Medellin, establishing them as a family unit with inheritance rights.