The family is suing the home's previous owners for not telling them about it before the sale, claiming they had received letters too.
In letters "the Watcher" wrote that the home "has been the subject of my family for decades."
"I asked [the previous owners] to bring me young blood," the Watcher wrote.
Content from the letters are included in a complaint filed to a New Jersey Court. The house is worth $1.3m (Â£826,131).
The stalker wrote that he has been in control of the house for two decades and he asked the previous owners to sell it.
"You have changed it and made it so fancy...it cries for the past and what used to be in the time when I roamed its halls," the stalker wrote. "And now I watch and wait for the day when the young blood will be mine again."
Westfield mayor Andy Skibitsky, speaking at town hall meeting in Westfield on Tuesday, said "The Watcher" is a mystery, ABC News reports.
"When, over a year ago, this matter was reported to the police, our police department conducted an exhaustive investigation," Mr Skibitsky said. "Such efforts, however, have not yielded information leading to charges being filed and, therefore, this case is pending introduction of any new evidence."
A New Jersey family will not move into their new million-dollar home after receiving threatening packages from a mysterious sender called "the Watcher".