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Open Facebook. Click your name. Click Photos. Click the Albums tab. Select an album. Select a picture you want to move. Click the pencil icon. Click Move to Other Album. Choose a new album. Click Move Photo.

Article:
Go to https://www.facebook.com/. This will open your Facebook News Feed if you're logged in.  If you aren't logged in, enter your email address (or phone number) and password in the top-right side of the page. You can only perform this method on desktop. This tab is in the top-right side of the Facebook page. Doing so takes you to your Facebook Timeline. It's below your cover photo on your profile page. This option is below and to the right of the "Photos" heading. Click an album from which you'd like to move a photo. Keep in mind at the album you choose must be one you created, not a Facebook-created album. For example, you can't move photos from the "Timeline Photos" album. Hover your mouse cursor over the picture you want to move. You'll see a pencil-shaped icon appear in the top-right corner of the photo's thumbnail. Doing so prompts a drop-down menu. It's near the bottom of the drop-down menu. Clicking this brings up a pop-up window. Click the drop-down box below the "Select another album for this photo:" heading in the pop-up window, then click an album to which you'd like to move the photo. You can only select a user-created album (again, not a Facebook-created one). This blue button is at the bottom of the window. Doing so will remove your photo from its current album and move it to your specified album. If you want to move multiple photos, you'll need to repeat this process for each photo you want to move.