According to the Apple support site, yes:

Apps from the Mac App Store may be used on any Macs that you own or control for your personal use.

See also:

If I have already downloaded an app from the Mac App Store, can I redownload it for free?

Yes. You can redownload apps from the Mac App Store as long as the app remains available. You may be asked to enter the Apple ID and password you initially used to download the app.

The key is to use the same Mac App Store account/login on all your computers. Then you can download and install apps on all your computers, regardless of which one you bought the application on.

So what are you waiting for, go forth and upgrade!