The couple, who were married on Saturday at Simpson's parents home in Encino, CA, spent their first night as husband and wife in a safari tent on the property before leaving for their honeymoon.
The day after the wedding, Wentz told PEOPLE, "We are going to a very, very, very, very private island so that the paparazzi can't follow us."
The couple's rep confirms to PEOPLE that Wentz is in New York City for business. Sources say the pair are also expected at a private party in the city.
Simpson's sister Jessica, who served as maid of honor at the wedding, arrived home in Los Angeles Thursday night after vacationing with her parents in Cabo San Lucas, Mexico.