try this:

$('<img/>').attr('src', 'http://picture.de/image.png').on('load', function() {
   $(this).remove(); // prevent memory leaks as @benweet suggested
   $('body').css('background-image', 'url(http://picture.de/image.png)');
});

this will create a new image in memory and use load event to detect when the src is loaded.

EDIT: in Vanilla JavaScript it can look like this:

var src = 'http://picture.de/image.png';
var image = new Image();
image.addEventListener('load', function() {
   body.style.backgroundImage = 'url(' + src + ')';
});
image.src = src;

it can be abstracted into handy function that return a promise:

function load(src) {
    return new Promise((resolve, reject) => {
        const image = new Image();
        image.addEventListener('load', resolve);
        image.addEventListener('error', reject);
        image.src = src;
    });
}

const image = 'http://placekitten.com/200/300';
load(image).then(() => {
   body.style.backgroundImage = `url(${image})`;
});

I have a jQuery plugin called waitForImages that can detect when background images have downloaded.

$('body')
  .css('background-image','url(http://picture.de/image.png)')
  .waitForImages(function() {
    alert('Background image done loading');
    // This *does* work
  }, $.noop, true);

There are no JS callbacks for CSS assets.