If the connection strings are in the configuration, you should be able to change the connection strings in the configuration. If it is not, you will need to edit the SSIS package using BIDS. Here is some info on where to look for the configuration: http://msdn.microsoft.com/en-us/library/cc671628.aspx
you just need to add a config file if not already present and identify connection string as a configurable item inside it. Then depending on whether you chose to store config as a file or inside table you can edit the file or run an update query on the table to change dtabase information to make it point to new database. You can also set this property from within sql server agent job step properties.