The Australian pair told the celebrity magazine People that they were "blessed to share almost three decades together".
The statement read, "Our journey is changing and we have chosen to separate to seek our individual growth.
On the Correlli TV set in 1995, Jackman and Furness first connected.
When they first met, Furness was a well-known actress, and Jackman had just graduated from theater school.
Their two adopted children, who are now 23 and 18, were born after they wed in April 1996.
The pair stated that their "family has been and always will be our highest priority" in a statement that appeared in People.
"With appreciation, love, and kindness, we start this new chapter. As our family navigates this adjustment in our lives, we sincerely appreciate your understanding and respect for our privacy.
"This is the only statement either of us will make," the couple concludes.
The Greatest Showman and Les Miserables star Jackman, who is best known for his appearances as Wolverine in the X-Men movies and its spinoffs, has frequently commented on social media about his love with Furness.
In April, on their previous wedding anniversary, he told Deb: "I love you. Our 27th wedding anniversary is today. 27 YEARS!!
"I adore you a lot. Together, we have built a lovely family. plus life. I am so grateful for your fun, spirit, generosity, wit, cheek, bravery, and loyalty.
I'm saying, "I love you with all my heart."
Their marriage was described as "natural as breathing" in a message he made on their silver wedding anniversary in 2021.
At the Wimbledon tennis tournament in London in July, the couple was seen together as they watched Carlos Alcaraz battle Novak Djokovic.
Following testing for skin cancer, Jackman announced to his followers on social media in April that he had been given the all-clear.
The actor underwent at least six treatments after having his initial skin cancer removed in 2013.