The 13,000-year-old object is on show as the centrepiece of an exhibition celebrating Ice Age Llandudno.
The bone was found at the Great Orme in the 1870s by a retired copper miner who polished pebbles to sell to tourists.
Dr Jill Cook of the British Museum said it was "very special" to reunite it with other rare items found there.
The decorated bone has been in London as part of the British Museum's display of Ice Age art almost continuously since its discovery around 140 years ago.
Decorated deer foot bones and perforated animal teeth found at the same site are also being loaned to Llandudno Museum by National Museum Wales.
New research by the British Museum has shown that the art and burial items found in Llandudno belonged to people who migrated into Britain 13,000 to 14,000 years ago, during the last Ice Age.
They arrived in north Wales with jewellery made from bear, deer and wild cattle teeth in the same style as those found in Belgium and France.
But they also had their own distinctive style, shown by the decoration of the horse jaw and the deer foot bones.
At this time, the Great Orme was not by the sea but dominated a wide coastal plain.
It had views over the coast, hills and distant mountains - an ideal place for people living by hunting and gathering.
The skeletons of three adults and a young person were also found in the cave, but few tools, suggesting Kendrick's Cave was a rare example of an Ice Age burial place.
The bones and teeth were found by accident by retired copper miner Thomas Kendrick, who used a cave on the Great Orme as a workshop to cut and polish pebbles to sell to tourists as souvenirs.
Dr Jill Cook, deputy keeper of prehistory and Europe at the British Museum, said the items were of international significance.
"The decorated horse chin from Kendrick's Cave is a reminder of our deep history," she said.
"It is usually on display in the British Museum with Ice Age art from France. Seeing it reunited with the other rare items found on the Great Orme is very special and a great start to Llandudno's plans to develop its museum."
The exhibition is backed by Â£37,000 from the Â£1.7m Cadw-funded Our Heritage Project aimed at boosting tourism in Gwynedd, Conwy and Snowdonia.
The items were previously on show at Llandudno Museum in 2008 and 2010.
Museum chair Roy Haley said: "We are very excited to welcome this rare and internationally important object back to Llandudno.
"Thanks to the support of the Our Heritage project, we have been given the opportunity to display a first-class collection that helps to tell the story of Llandudno - and we hope to see many more visitors as a result."
Phil Edwards, Conwy council cabinet member for communities, added:  "The objects from Kendrick's Cave offer a unique and fascinating insight into our distant past here in Llandudno."
Ice Age Llandudno runs at the town's museum until 30 September.

The Woodland Trust wants to buy the land at Llennyrch woodland.
Natural Resources Wales (NRW) has given £50,000 but a further £750,000 is needed and a campaign will be launched on Tuesday at the National Eisteddfod in Meifod, Powys.
The charity said the area has been called a "Celtic rainforest" and it wants to improve wildlife on the site.
NRW chief executive Dr Emyr Roberts said: "This is a fantastic opportunity to bring the whole woodland area under conservation management."
The total cost of the project is £1.5m and the rest of the cost will be met by money left to the Woodland Trust.
A horse's jaw bone, which features what is believed to be the oldest work of art in Wales, has returned to the town where it was found in a cave.
[NEXT_CONCEPT]
A conservation charity is trying to raise £800,000 to purchase 550 acres of land in Snowdonia National Park.