The attached file contains a script that creates a stored procedure called MoveDatabase, that will enable you to logically move a database and its objects to another server.  Create the stored procedure in the source control database.

Naturally, the destination server needs to exist first so you'll need to add the server to the project if it isn't already part of it.  Once that's done you can execute the following script, remembering to enter the correct values for the 4 parameters near the top.

Although I doubt its necessary as the procedure is pretty straight forward it's always a good idea to backup the source control database if you don't already do it regularly.

declare @current_server_db_id int;
declare @destination_server_id int;
declare @current_server varchar(128);
declare @database varchar(128);
declare @project varchar(128);
declare @destination_server varchar(128);

select @current_server = '<enter current server name>'
  , @database = '<enter database name>'
  , @project = '<enter project name>'
  , @destination_server = '<enter destination server>'

select @current_server_db_id = ServerDbId
from ProjectServerDatabase psd
 join ProjectServer ps on ps.ProjectServerId = psd.ProjectServerId
where ServerName = @current_server
and DatabaseName = @database
and ProjectName = @project

select @destination_server_id = ProjectServerId
from ProjectServer
where ServerName = @destination_server
and ProjectName = @project

exec MoveDatabase @current_server_db_id, @destination_server_id