The remains were unearthed at Kapsomin in the Tugen hills in Kenya's Baringo district.
The creature is said to be six million years old, double the age of the previous record holder, an australopithecine skeleton commonly referred to as Lucy.
The team said its hominid was more human than Lucy, with teeth close to those of modern humans and a strong femur, suggesting an ability to walk upright.
"Such a finding radically alters scenarios about human origins," the team said at a conference in Paris, arguing that Lucy might not have been a direct forerunner of modern man, but a more distant cousin.
Reserved judgement
The conference was the first to be held in Europe by the team, all members of the Kenya Palaeontology Expedition (KPE), since it first announced the fossil discovery last month.
The remains were unearthed at Kapsomin in the Tugen hills in Kenya's Baringo district.
Professor Chris Stringer, of the Natural History Museum in London, UK, said the science community would wait until the team had published its results in an academic journal before assessing the fossils' significance.
"The fossils are potentially of great importance," he told BBC News Online.
'Millennium Ancestor'
The creature is being called the "Millennium Ancestor" and consists of 13 pieces, including a piece of jaw with some teeth, a fingertip, an arm, and the crucial sturdy leg bone.
Some palaeontologists have said the fragments are too piecemeal to justify the team's claims. But the finding has also proved controversial for more than scientific reasons.
The team, led by Martin Pickford and Brigitte Senut, has been criticised for taking the fossils out of Kenya, and has been involved in a row with another group about digging rights.
Details of the fossils will be published in English in a French journal, Comptes Rendus de l'Academie des Sciences.