var img = new Image();
img.onload = function() { alert("Height: " + this.height); }
img.src = "http://path/to/image.jpg";
Note that it's important to do it in the order above: First attach the handler, then set the src. If you do it the other way around, and the image is in cache, you may miss the event. JavaScript is run on a single thread in browsers (unless you're using web workers), but browsers are not single-threaded. It's perfectly valid for the browser to see the src, identify the resource is available, load it, trigger the event, look at the element to see if it has any handlers that need to be queued for callback, not see any, and complete the event processing, all between the src line and the line attaching the handler. (The callbacks wouldn't happen between the lines if they were registered, they'd wait in the queue, but if there aren't any, the event isn't required to wait.)
I had a slow CAPTCHA (1st_image) image loading on my page and I wanted to display another image (2nd_image) only AFTER the CAPTCHA image (1st_image) is loaded. So I had to wait for the CAPTCHA (1st_image) image to load first.
Here is the solution that works perfectly fine to wait for an image to load first and then load another image (don't forget to display a "please wait!" image while they are waiting for other image to load):
Either the Internet speed is slow or fast, and the browser will wait for the whole page to load with all the images (even if they are linked externally) and then execute the function, so the second image is displayed only after the first image loads fine.
Advanced note: You can use a web page URL in the "src" of the image to load a web page first and then show the image. The purpose is to load the cookie from the external webpage which might effect the second image displayed (like CAPTCHA).
The accepted answer is outdated but does show the basic Image#onload callback approach. Nowadays, you'll likely want to promisify the image load to avoid callback hell.
This answer is a good shot at promisifying the image onload handler, but is missing some key points as my comment indicates.
Here's another promisification of Image that is a bit more general. Rejecting in the onerror handler and passing the actual image object into the resolver are important to make the function minimally reusable.
Improvements might include additional parameters (such as crossOrigin, for example). A settings object or providing an Image as a parameter is another approach to generalize the function (setting src fires the request, so that should go last after handlers have been added).
With the above function, Promise.all can be used to load a batch of images in parallel (Promise.allSettled is useful if you want to keep going even if some images don't load).