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.
A body found in the ruins of a collapsed building at Didcot Power Station has been identified.