Christopher Huxtable, 34, from Swansea, had been missing since the collapse in February.
His body was found on Wednesday and workers who carried out the search formed a guard of honour as it was driven from the site in the early hours of the morning.
Ken Cresswell, 57, and John Shaw, 61, both from Rotherham, remain missing.
The body of a fourth man, Michael Collings, 53, from Brotton, Teesside, was previously recovered from the site.
Swansea East MP Carolyn Harris, who has been involved with the family since the incident, said they still did not know all the facts about the collapse.
She said: "I feel very sad. My heart and my prayers go out to the family who have waited desperately for Christopher's body to be found. They can finally have closure, and say goodbye to him and grieve his loss.
"But let's not forget that there's two other families who are still waiting for their loved ones to be returned."
The building was due for demolition when it partially collapsed in February.

Scientists say the new species is a member of the group that gave rise to crocodiles and dinosaurs.
The reptile lived at a time when the Earth was recovering from a mass extinction that wiped out most animals.
The discovery may shed light on how the group of animals evolved and spread.
About 252 million years ago, a mass extinction devastated life on land and in the oceans. Some 90% of species disappeared.
At the time, the Earth was very different from today, with continents grouped into the supercontinent, Pangaea.
Researchers led by Eudald Mujal of Universitat Autònoma de Barcelona, Spain, examined fossilised footprints from about 247 to 248 million years ago found in the Pyrenees mountains in Catalonia.
They found most tracks were made by the ancestors of crocodiles and dinosaurs, a group known as archosauromorphs.
Most footprints were small, about half a metre in length, although a few were longer than three metres.
Among them was a new footprint that is thought to be a new species of reptile, Prorotodactylus mesaxonichnus.
The makers of the footprints could belong to the Euparkeria, a group of dinosaur relatives known from the same time period in Poland, Russia, China and South Africa.
Co-researcher Josep Fortuny of the Institut Català de Paleontologia Miquel Crusafont said the footprints suggest the animals, measuring around half a metre, used all four limbs to walk and often also left marks with their tails.
"Some footprints point to the possibility of bipedal locomotion in specific moments with the aim of moving faster," he said.
The researchers think archosauromorphs dominated the river beds of the ancient Pyrenees.
The group may have been key to the recovery of ecosystems after the extinction, going on to spread across the supercontinent.
"These tracks represent the first evidence of the vertebrate recovery of the End-Permian extinction," Eudald Mujal told BBC News.
He said the search was underway for fossilised bones of the animals that made the tracks.
The research is published in the journal, PLOS ONE.
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A body found in the ruins of a collapsed building at Didcot Power Station has been identified.
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The footprints of a mysterious reptile that lived about 250 million years ago have been identified in fossils from the Pyrenees mountains.