Configuring Exim to use Gmail as a Smarthost.

Add a router before or instead of the dnslookup router:

gmail_route:
  driver = manualroute
  transport = gmail_relay
  route_list = * smtp.gmail.com

Add a transport:

gmail_relay:
  driver = smtp
  port = 587
  hosts_require_auth = <; $host_address
  hosts_require_tls = <; $host_address

Add an authenticator (replacing myaccount@gmail.com and mypassword with your own account details):

gmail_login:
  driver = plaintext
  public_name = LOGIN
  hide client_send = : myaccount@gmail.com : mypassword

$host_address is used for hosts_require_auth and hosts_require_tls instead of smtp.gmail.com to avoid occasional 530 5.5.1 Authentication Required errors. These are caused by the changing IP addresses in DNS queries for smtp.gmail.com. $host_address will expand to the particular IP address that was resolved by the gmail_route router.

<; is required for the hosts_require_auth and hosts_require_tls lists because $host_address can contain colons (the default list separator character) when sending with IPv6.