All of Canon's EF and EFS lenses fit the 60D.
Therefore you can use them for video.
Simple.
In fact any lens that fits the 60D (Canon, Tamron , Sigma, etc..) can be used for stills or video.
Remember that once the video has started you can't autofocus... you'll have to do what the pro's do and use the manual focus.
In video mode go to the menu and set Movie Exposure to manual.
Assuming you are going to film in 1080 HD at 24 fps, set your shutter speed to 1/50.
(If your filming at 30fps, you'd set the shutter speed to 1/60).
Using the Live View adjust the f-stop and/or ISO to get correct exposure.
You can then half press the shutter to get the first focus if you need to.
Press the red button on the back and film away.
Manually focus now as required... this takes a bit of practice on the live view screen but you soon get used to it.
Also on the 3rd Menu page your Picture Style will affect the final video.
If you want the camera to Autofocus you'll be better off with the 70D. But even then AF in video is only possible with the new STM lenses. Any other lens still requires manual focus.