"We have been blessed to share almost three decades together as husband and wife in a wonderful, loving marriage. Our journey now is shifting and we have decided to separate to pursue our individual growth," the two Australians said in the joint statement.
Their separation was first reported by People magazine.
They said the statement would be their only one on their break-up and that their family is their highest priority. They will undertake "this next chapter with gratitude, love and kindness".
A representative confirmed the statement to the Associated Press on Friday.
The couple met in 1995 on the set of an Australian television show where both were actors.
Furness at the time was the more established of the two.
They married in 1996 and had two children: Oscar, now 23, and Ava, now 18.
Jackman also ascended to become a major star in Hollywood and on Broadway.
In April, Jackman celebrated their 27th anniversary with a tribute on Instagram.
"I love you so much. Together we have created a beautiful family. And life," he wrote.
"Your laughter, your spirit, generosity, humour, cheekiness, courage and loyalty is an incredible gift to me."
The couple have been red carpet mainstays for years, posing together at the Oscars, at Broadway events and at the Met Gala, including the most recent edition in May.
They attended Wimbledon together in July.
Furness, 67, is an advocate for orphans and adoption, especially in her native Australia, and one of the founding members of National Adoption Awareness Week.
Jackman, 54, who played the superhero Wolverine in several movies, is reprising the role in Deadpool 3, which is on hold due to the actors strike.
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