The ship belonging to Spanish NGO Proactiva Open Arms arrived in the southern port of San Roque, just across from Gibraltar near the city of Algeciras, at 9:20 am (0720 GMT).
Journalists were refused access and kept at a distance.
Madrid said the migrants, nearly all from Sudan, would not be given a special 45-day humanitarian residency permit like those on board the Aquarius received.
According to Proactiva, the 75 men and 12 boys had spent 50 hours at sea on board an inflatable boat under intense heat without drinking water and many suffered burns from a mixture of fuel and salt water before they were rescued on August 2.
The migrants "probably could not have survived another day," the operations coordinator of the NGO, Gerard Canals, told a news conference.
The NGO says many of them had been "repeatedly abused in Libya."
The ship spent days wandering the Mediterranean as it waited for a port to dock.
Finally madrid stepped in after Rome refused access, even though Spain has overtaken Italy as the main destination for migrants this year due to a crackdown by Libyan authorities and the new Italian government's hardline approach to migrants.
Italy had been asking in vain for years for more help from the EU to manage the arrival of migrants. For the past two months it has been governed by a coalition of far-right and populist parties and now refuses to allow ships that rescue migrants in the Mediterranean to dock in its ports.
France will take in about 20 of the 87 migrants who arrived in Spain "in the spirit of European solidarity," a government spokesman in Paris said.
More than 23,700 people have arrived in Spain by sea so far this year with 307 dying in the attempt, according to the International Organization for Migration -- more than during all of last year.
No special treatment
The country's new Socialist government has allowed the docking of three NGO rescue ships since June after Italy and Malta refused access.
In June, the French NGO Aquarius ship, which had picked up 630 stranded migrants off Libya, was allowed to dock in Spain's eastern port of Valencia.
Then on July 4, a Proactiva Open Arms' ship docked in Barcelona with 60 migrants.
When the Aquarius docked, Madrid had given each migrant a 45-day residency permit for humanitarian reasons.
Those brought back to Barcelona were also given special treatment.
This time round though, the Spanish government has said the 87 migrants who have arrived in San Roque will be treated in the same way as the hundreds who arrive every week on Spanish shores.
Faced with the arrival of hundreds of migrants, the welcome centres in the Cadiz province of Andalucia, where San Roque is located, cannot cope.
Migrants have had to sleep on board coastguard boats or in sports centres.
'Don't have the means'
Jose Ignacio Landaluce, the conservative mayor of Algeciras, told Spanish radio he was "concerned" at the idea that his 125,000-strong city would become "the only port welcoming rescue boats and NGO ships."
He stressed that migrants were arriving almost daily in his city on board rickety inflatable dinghies, 500 on Tuesday alone.
"We in Algeciras and the rest of Spain all have a heart, but you have to be reasonable, we just don't have the means," he added, pointing to high unemployment in his city.
Spain's new Socialist government has blamed the previous conservative adminstration, which it ousted in June, for not having prepared for the mass arrival of migrants, pointing out the problem started more than a year ago.
The conservatives in turn accuse government of creating a "pull factor" by taking in the rescue ships.
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
![Lori and George Schappell shared 30% brain [Shutterstock]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Lori and George Schappell shared 30% brain [Shutterstock]")
