The young migrants forced their way through the high border fence into the Spanish North African territory, ecstatic to have finally crossed into a European Union state.
Some kissed the ground and shouted "Thank you lord" and "Viva Espana", although several had bloodied hands and feet as well as torn clothes after making it through the barrier.
Ceuta and Melilla, also a Spanish territory in North Africa, have the EU's only land borders with Africa, so are entry points for migrants who either climb the border fence, swim along the coast or hide in vehicles.
"356 managed to get in out of a total of around 700" who attempted entry, a spokesman for the local authority said. "They entered after breaking access gates with shears and hammers."
Their arrival came just days after nearly 500 migrants made it over the fence on Friday, one of the biggest entries since the border barrier was reinforced in 2005.
It also comes amid a dispute between Morocco and the EU over the interpretation of a free trade farm and fishing deal.
In a late 2016 ruling, an EU court said the deal did not apply to the Western Sahara, a former Spanish colony controlled by Rabat where the Polisario Front is fighting for independence.
The court said this was because the status of the disputed territory remained unclear according to the international community.
The 28-nation bloc did not recognise it as part of Morocco.
The ruling opened the way for the Polisario Front and its supporters to contest trade in products from the Western Sahara between Morocco and the 28 EU states.
The decision angered Morocco, which on February 7 suggested it could lead to "a new flow of migration" towards Europe and place the continent "at risk".
The last such massive attempt took place on New Year's Day when more than 1,000 migrants tried to jump a high double fence between Morocco and Ceuta in a violent assault that saw one officer lose an eye.
The enclave has been ringed by a double wire fence eight kilometres long. The six-metre high fence also has rolls of barbed wire.The young migrants climbed over the high border fence into the Spanish North African territory, ecstatic to have finally crossed into a European Union state.