To quickly answer the question, as of the time of writing, yes, but make sure to use other additional image formats as fallback so that everyone can view your images.
If you are are unsure what WebP is, WebP is a fairly new (announced on September 30th 2010) image format (like jpg, and png). Since September 2010 Google has being adding and experimenting with different things that other image formats have (like animation, ICC profile, XMP metadata, lossless compression) and other things which makes the image more appealing to be used, and makes the image be supported on more browsers.
Now that you briefly what WebP is, it’s time to talk about if it’s ready to be used on websites. You may be thinking “It’s been announced for 8+ years at this time so clearly all website browsers like Internet Explorer, Firefox, Chrome, and Safari should be able to display the image perfectly” and while some browsers (like Edge, Firefox, and Chrome) have supported WebP for years there are still some browsers that don’t support it at all (like Internet Explorer, Safari, iOS Safari just to name a few). This can change with time so it is suggested to pay attention to caniuse.com to see when those unsupported browsers finally do support WebP.
What do you do then if you want to use WebP on your website, but want to make sure all your website visitors can view your images? Have other images as a fallback. How your website does this depends on what platform your site is on (WordPress is an example of one) and what other things like plugins are on your website. You will need something that will create WebP images for you (like ShortPixel (affiliate link) or CloudConvert), then you will need something to show that there are WebP images and what images are available as fallback (if you use a plugin to convert your images to WebP it may have an option you can select, or inside your cache options you may be able to select it).
There are some website platforms that don’t currently support WebP (like Squarespace, or Wix) and some platforms don’t allow you to upload you to currently upload WebP (like WordPress) but more website platforms are supporting WebP as time goes on so check your platform’s forums to see what talk there is about WebP. If you can’t find anything in the forums consider contacting the support team and see if they have thought about WebP and what their progress is.
Considering all the time you can spent on this how do you know if your website is showing WebP images? There are a few ways to check, first is to make sure you have a browser that supports WebP (use the latest version of Firefox or Chrome to be sure), second make sure you have cleared the website cache (so that you can be sure you actually see the WebP images, how you do this depends on your website platform), third is to check a page where images are placed to see if WebP images are loading (there are many ways to do this check, ShortPixel and Imagify both provide slightly different ways). You may think that there would be a website where you could put in your website and it would tell you if your website is using WebP images but currently there is no such site because depending what you are using on your site, your site may display an different image format (it may display the best one that best fits the browser).
To conclude, WebP is a fairly new image format that is great to have on your website but you will need to change a few things in order to have the WebP images be shown and be able to have the images shown for those who can’t view WebP images.