Handling growing number of Tenants in Multi-tenant Database Architecture
At the lower end (500 tenants / 10000 users) this is how I did it. First, you have a "control" database that is global, central and contains all of the information about tenants and users (I really don't think you want to manage these as SQL auth logins). So imagine a database called "Control" with the following tables:

CREATE TABLE dbo.Instances
(
  InstanceID INT PRIMARY KEY,
  Connection VARCHAR(255)
  --, ...
);

INSERT dbo.Instances SELECT 1, 'PROD1\Instance1';
INSERT dbo.Instances SELECT 1, 'PROD2\Instance1';
-- ...

CREATE TABLE dbo.Tenants
(
  TenantID INT PRIMARY KEY,
  Name NVARCHAR(255) NOT NULL UNIQUE,
  InstanceID INT -- Foreign key tells which instance this tenant's DB is on
  --, ...
);

INSERT dbo.Tenants SELECT 1, 'MyTenant', 1;
-- ...

CREATE TABLE dbo.Users
(
  UserID INT PRIMARY KEY,
  Username VARCHAR(320) NOT NULL UNIQUE,
  PasswordHash VARBINARY(64), -- because you never store plain text, right?
  TenantID INT -- foreign key
  --, ...
);

INSERT dbo.Users SELECT 1, 'foo@bar.com', 0x43..., 1;


In our case when we added a new tenant we would build the database dynamically, but not when the admin user clicked OK in the UI... we had a background job that pulled new databases off a queue every 5 minutes, set model to single_user, and then created each new database serially. We did this to (a) prevent the admin user from waiting for database creation and (b) to avoid two admin users trying to create a database at the same time or otherwise getting denied the ability to lock model (required when creating a new database).

Databases were created with the name scheme Tenant000000xx where xx represented Tenants.TenantID. This made maintenance jobs quite easy, instead of having all kinds of databases named BurgerKing, McDonalds, KFC etc. Not that we were in fast food, just using that as an example.

The reason we didn't pre-allocate thousands of databases as the comment suggested is that our admin users usually had some idea of how big the tenant would become, whether they were high priority, etc. So they had basic choices in the UI that would dictate their initial size and autogrowth settings, which disk subsystem their data/log files would go to, their recovery settings, backup schedule to hinge off of, and even smarts about which instance to deploy the database to in order to best balance usage (though our admins could override this). Once the database is created, the tenant table was updated with the chosen instance, an admin user was created for the tenant, and our admins were e-mailed the credentials to pass along to the new tenant.

If you're using a single point of entry, it is not feasible to allow multiple tenants to have users with the same username. We opted to use e-mail address, which - if all users work for the company and use their corporate e-mail address - should be fine. Though our solution eventually became more complex for two reasons:


We had consultants that worked for more than one of our clients, and needed access to multiple 
We had tenants who themselves were actually comprised of multiple tenants


So, we ended up with a TenantUsers table that allowed one user to be associated with multiple tenants. 

Initially when a user logs in, the app will know the connection string for the control database only. When a login is successful, it can then build a connection string based on the information it found. E.g.

SELECT i.Connection
  FROM dbo.Instances AS i
  INNER JOIN dbo.Tenants AS t
  ON i.InstanceID = t.InstanceID
  INNER JOIN dbo.TenantUsers AS u
  ON i.TenantID = u.TenantID
  WHERE u.UserID = @UserID;


Now the app could connect to the user's database (each user had a default tenant) or the user could select from any of the tenants they could access. The app would then simply retrieve the new connection string, and redirect to the home page for that tenant.

If you get into this 10MM user area you propose, you'll definitely need this to be balanced better. You may want to federate the application so that they have different points of entry connecting to different control databases. If you give each tenant a subdomain (e.g. TenantName.YourApplicationDomain.com) then you can do this behind the scenes with DNS/routing without interrupting them when you need to scale out further.

There is a lot more to this - like @Darin I am only scratching the surface here. Let me know if you need a non-free consult. :-)