Still, there's no way Wolverine is gone forever
Here's a safe prediction: this is not the last time you'll see Wolverine in a movie. Loopy continuity, wonky resurrections, and alternate timelines are the norm in comics, and as the first-wave of modern comic book stars age out of their signature roles, movie studios will find ways to recast these parts just like they've done in the past. Look at Superman. Or Batman. Or Spider-Man. Or the Hulk. If anything, Jackman, along with Robert Downey Jr., is the outlier for having lasted so long in one role.
As long as Wolverine remains a badass with claws in his hands, there will always be a demand for him. Though Fox has attempted to carve out a bub-less lane for the X-Men films to expand beyond the spiky haired tough guy, he's still an icon. Jackman's often swaggering, occasionally grief-stricken portrayal made him the cigar-chomping face of the franchise, but there's no reason another actor won't be able to put their spin on it at a later date and even Jackman agrees. "The character will go on,” he told the Times. “Someone else will play it, for sure.”