Redirect the emails from domain2 to domain1

[Quaquaraquà]

Dear Dovecot and Exim users,

I have a VPS using these two applications. I am transitioning from a 
domain_old to a domain_new. I'd like to redirect all the emails from 
domain_old to the local mailboxes of users @ domain_new.  In exim I've 
assumed that it is enough to add domain_old to the list of local domains:

domainlist local_domains = @ : domain_new : domain_old
...
begin routers
...
local_users:
   debug_print = "R: local_user for $local_part@$domain"
   driver = accept
   domains = +local_domains
   transport = dovecot_lmtp
   cannot_route_message = Unknown user

However in Dovecot I'm checking both the username and the domain to 
perform the authentication:
auth_username_format = %Lu
passdb { driver = sql ; }
password_query = SELECT username, domain, password FROM users WHERE 
username = '%n' AND domain = '%d'

To have this system to work, I wish some special rule that rewrites the 
domain from domain_old to domain_new. But I'm not sure whether this 
needs to be done in exim or dovecot and how to add it?

- Quaquaraqua'