If your Future is the result of a call to an ExecutorService method (e.g. submit()), the easiest would be to use the CompletableFuture.runAsync(Runnable, Executor) method instead.
From
Runnbale myTask = ... ;
Future<?> future = myExecutor.submit(myTask);
to
Runnbale myTask = ... ;
CompletableFuture<?> future = CompletableFuture.runAsync(myTask, myExecutor);
The CompletableFuture is then created "natively".
EDIT: Pursuing comments by @SamMefford corrected by @MartinAndersson, if you want to pass a Callable, you need to call supplyAsync(), converting the Callable<T> into a Supplier<T>, e.g. with:
CompletableFuture.supplyAsync(() -> {
    try { return myCallable.call(); }
    catch (Exception ex) { throw new CompletionException(ex); } // Or return default value
}, myExecutor);
Because T Callable.call() throws Exception; throws an exception and T Supplier.get(); doesn't, you have to catch the exception so prototypes are compatible.
A note on exception handling
The get() method doesn't specify a throws, which means it should not throw a checked exception. However, unchecked exception can be used. The code in CompletableFuture shows that CompletionException is used and is unchecked (i.e. is a RuntimeException), hence the catch/throw wrapping any exception into a CompletionException.
Also, as @WeGa indicated, you can use the handle() method to deal with exceptions potentially being thrown by the result:
CompletableFuture<T> future = CompletableFuture.supplyAsync(...);
future.handle((ex,res) -> {
        if (ex != null) {
            // An exception occurred ...
        } else {
            // No exception was thrown, 'res' is valid and can be handled here
        }
    });