Cordless phones - different brand handsets?

Can I join two different brand handsets? We already have AT&T (5.8 ghz) base and 3 handsets. We won in a raffle Uniden base + 2 handsets. Can we join the Uniden handsets to our AT&T base? I know that there's a process to register handsets to the base. I don't want to open (and break the seals on)the box if it's not going to work.