"We can confirm that Joel Taylor has passed away while on a cruise," the statement read.
The family released the statement through Richard L. Duggar II, the owner of the Martin-Duggar Funeral Home in Taylor's native Oklahoma, though their relationship was not immediately clear.
The cause of Taylor's death is still unknown, the family said.
The family asked for privacy in the wake of Taylor's death.
"We ask for your understanding during this difficult time and your respect for the family while they deal with the loss of their son," it read.
Taylor, who was 38 years old, was reportedly aboard a Royal Caribbean cruise ship when his body was discovered on Tuesday.
Royal Caribbean did not immediately return a request for comment, but the cruise line released a statement to People magazine, which read, “As is our standard procedure, law enforcement was notified and responded to the ship when it arrived in San Juan, Puerto Rico, on Tuesday, January 23."
"We extend our most sincere and heartfelt condolences to the family and friends of the 38-year-old male guest from the United States who died while onboard Harmony of the Seas," its statement continued. "A member of our Care Team is providing support and assistance to his family."
The San Juan, Puerto Rico, division of the U.S. Coast Guard is investigating Taylor's death.
"While we do not have all the details at this time, the Coast Guard is conducting a preliminary investigation following up on the report made by the cruise ship and in cooperation with the FBI, local authorities and industry partners to look into this incident," it said in a statement.
Meanwhile, Taylor's friend Reed Timmer was the first to speak out about the news of his friend's death.
"RIP my best friend and storm chasing partner, Joel Taylor," he tweeted late Tuesday. "I am shocked and absolutely devastated by the loss of my incredible, caring friend. We chased so many intense storms, and I wish we could have just one more storm chase. I'll miss you forever, Joel. We lost a legend."
Discovery Channel, the network that launched Taylor into stardom years ago on "Storm Chasers," also released a statement to ABC News about the meterologist's death.
"We are so saddened to hear about Joel’s passing. We will always remember him fondly as an incredible meteorologist and driver of 'The Dominator.' Our thoughts and prayers are with his family and friends at this difficult time," a spokeswoman for the network stated.
Taylor was featured on Discovery from 2008 until 2012.