Luckily it's easy to convert to CompletableFutures and back. Let's take Spring 4 ListenableFutures as an example. How to convert it to CompletableFuture?

static <T> CompletableFuture<T> buildCompletableFuture(
		final ListenableFuture<T> listenableFuture
  ) {
  //create an instance of CompletableFuture
  CompletableFuture<T> completable = new CompletableFuture<T>() {
     @Override
     public boolean cancel(boolean mayInterruptIfRunning) {
        // propagate cancel to the listenable future
        boolean result = listenableFuture.cancel(mayInterruptIfRunning);
        super.cancel(mayInterruptIfRunning);
        return result;
     }
  };

  // add callback
  listenableFuture.addCallback(new ListenableFutureCallback<T>() {
      @Override
      public void onSuccess(T result) {
        completable.complete(result);
      }

      @Override
     public void onFailure(Throwable t) {
        completable.completeExceptionally(t);
     }
  });
  return completable;
}

We just create a CompletableFuture instance and add a callback to the ListenableFuture. In the callback method we just notify the CompletableFuture that the underlying task has finished. We can even propagate call to cancel method if we want to. That's all you need to convert to CompletableFuture.

What about the opposite direction? The approach is a bit different, but it's more or less straightforward as well

class ListenableCompletableFutureWrapper<T> implements ListenableFuture<T> {
    private final ListenableFutureCallbackRegistry<T> 
        callbackRegistry = new ListenableFutureCallbackRegistry<>();

    private final Future<T> wrappedFuture;

    ListenableCompletableFutureWrapper(
        CompletableFuture<T> wrappedFuture
    ) {
        this.wrappedFuture = wrappedFuture;
        wrappedFuture.whenComplete((result, ex) -> {
            if (ex != null) {
                if (ex instanceof CompletionException 
                    && ex.getCause() != null
                ) {
                    callbackRegistry.failure(ex.getCause());
                } else {
                    callbackRegistry.failure(ex);
                }
            } else {
                callbackRegistry.success(result);
            }
        });
    }

    @Override
    public void addCallback(
        ListenableFutureCallback<? super T> callback
    ) {
        callbackRegistry.addCallback(callback);
    }


    @Override
    public boolean cancel(boolean mayInterruptIfRunning) {
        return wrappedFuture.cancel(mayInterruptIfRunning);
    }

    @Override
    public boolean isCancelled() {
        return wrappedFuture.isCancelled();
    }

    @Override
    public boolean isDone() {
        return wrappedFuture.isDone();
    }

    @Override
    public T get() throws InterruptedException, ExecutionException {
        return wrappedFuture.get();
    }

    @Override
    public T get(long timeout, TimeUnit unit) throws InterruptedException, ExecutionException, TimeoutException {
        return wrappedFuture.get(timeout, unit);
    }
}

We just wrap the CompletableFuture and again register a callback. The only non-obvious part is the use of ListenableFutureCallbackRegistry which keeps track of registered ListenableFutureCallbacks. We also have to do some exception processing, but that's all.

If you need to do something like this, I have good news. I have wrapped the code to a reusable library, so you do not have to copy and paste the code, you can just use it as described in the library documentation.