A young humpback whale is “swimming free” after the mammal was entangled in ropes in Sydney Harbour for nearly 24 hours during a desperate rescue operation.

The difficult mission began on Thursday and ended late Friday morning when the whale in distress was cut free from the ropes wrapped around its tail.

The humpback whale, estimated to be between 10 and 15 metres long, swam directly towards the Sydney Heads and into the open sea.

Ben Khan, area manager of the NSW National Parks and Wildlife Service, said the mammal “swam free and broke free” after whale release specialists managed to cut the ropes.

The ship continued to be monitored by marine experts as it left port, he told reporters.

Jessica Fox of the volunteer rescue group ORRCA said it was common for whales to enter Sydney Harbour, but it was extremely rare for one to become entangled.

She told AAP it was not known how the whale got caught in the trap, but it happened before it reached port.

The “miraculous” release came after buoys were used to keep the animal relatively still while specialized personnel worked to free it.

As the whale swam between Bradley’s Head and Manly Headland, gamekeepers removed the ropes using a long pole tipped with special blades.

Citizens first noticed the injured whale on Thursday around 1 p.m. and reported it to the ORRCA hotline.

Khan said the service’s whale rescue team began work in the afternoon but was incapacitated by sunset.

“It’s obviously a very complicated operation. We have a live animal that is very, very large,” he said.

Authorities praised commercial vessels operating near the whale in Sydney Harbour, saying they adhered to exclusion zones so rescuers could free the entangled whale.

Humpback whales swim north to warmer waters in June and July and return south in September and November.

According to ORRCA, late September is the time when humpback whales most frequently pass through Sydney Harbour on their way south.

Humpback whales are the most commonly seen species off the coast of New South Wales and their numbers are increasing due to conservation efforts.