Yes.
All you need to do is connect it to the Ethernet port on the new computer, open a web browser and type the following into the address bar
http://192.168.0.1 and then login to the router using the username of admin and the password of password and then enter your ADSL username and password into the basic settings, click save and you should be good to go.
(the address and username/password are based on a netgear router but there are only minor differences for other braands)
It will also all be detailed in the instructions that come with it.