Anh Nhu Nguyen, of no fixed address, was charged with five counts on Thursday evening, Scotland Yard said.
Officers said the 52-year-old was remanded in custody and will appear at Westminster Magistrates Court.
He is the second man arrested in the wake of the fire, after a 43-year-old was detained for posting photos showing a victim’s body on social media.
Survivors made homeless by the disaster are being offered temporary housing and thousands of pounds in government funding and public donations to help them rebuild their lives.
The devastating fire at the 24-storey building in west London is believed to have claimed the lives of at least 80 people, with police warning they may not know the full death toll until the end of the year.
Detective Superintendent Fiona McCormack said earlier this week: “We are many months from being able to provide a number which we believe accurately represents the total loss of life inside Grenfell Tower.
“What I can say is that we believe that around 80 people are either dead or sadly missing and I must presume that they are dead.”
Meanwhile, a criminal investigation is taking place to establish if charges will be brought against those involved in renovating the building, including manslaughter.
“We are continuing to seize material on a daily basis and the number of companies and organisations that we know so far had played a role in the refurbishment is over 60,” Ms McCormack said.