Cayman Music and Blue Mountain Music had aired their dispute at a trial in London in May - and a judge yesterday delivered a ruling.
One song involved was No Woman, No Cry, one of the late Jamaican reggae star's most famous works.
The case centred on the "construction" of an agreement made in 1992 - 11 years after Marley's death - under which copyrights in "various musical works" were transferred by Cayman.
Cayman claimed that the 13 songs were not transferred under that agreement.
Blue Mountain, which is responsible for administering rights transferred under that agreement, disputed the claim.
Deputy High Court judge Richard Meade ruled against Cayman and dismissed the company's claim.
Lawyers for Cayman told the judge that Marley agreed a publishing deal with Cayman in late 1973.
They said the 13 songs were written by Marley between October 1973 and October 1976.
And they said Marley "fraudulently" attributed the songs to other people to avoid the provisions of the 1973 publishing agreement.
Lawyers for Blue Mountain said, on the "straightforward application of ordinary principles of contract law", the claim had to be dismissed.
They accepted that Marley "falsely claimed" that the 13 songs had been composed by other people in an attempt to "escape the automatic assignment of their copyright to Cayman".
But they said it was "common ground" that as a matter of law the "ruse was ineffective".
They said the "plain intention" of the 1992 agreement was to "transfer all rights".