Demolition originally began three and a half years ago on the building, which was heavily damaged in the September 11th attacks.
It was halted in August 2007 after firefighters Joseph Graffagnino and Robert Beddia died in a fire at the building when they were unable to get water out of a broken standpipe.
Mayor Michael Bloomberg signed two bills Wednesday, mandating increased testing and alarm systems for standpipes.
He said the new regulations will be vital to protecting both firefighters and construction workers.
"Testing of standpipe systems is currently required at the end of construction of a new building but not while a building is going up, and it's during the construction phase that some of the most dangerous activities and conditions arise and the same is true, obviously, when a building is coming down," Bloomberg said.
Decontamination work at the building was finished this past August.
Fifteen floors of the 41 story tower have already been taken down.