Out of the box, as you know, spring-boot expects its Datasource details to be using a specific set of variable names.  Being spring of course you can rework this if you need by a few methods:
1/ If the need to use variables from the environment comes from deployment to a cloud service such as Cloud Foundry or Horuku, there is spring-boot-starter-cloud-connector which handles allot of the plumbing out of the box.  A good read is the (Binding to Data Services with Spring Boot in Cloud Foundry article and the Deploying to the cloud docs which walks you thru this
2/ Instead of relying on Spring-Boot's own auto-magical wiring mechanism, you can create a custom configuration bean to override how the DataSource information is populated.  A good read explaining the annotations involved can be found here:  Spring Java Config Documentation - @Bean Configuration JavaDOC.   Based on your example above, here is what I spat out:
@Configuration
public class MyDataSourceConfig {
    @Bean
    @Primary
    public DataSource getDataSource() {
        String url = "jdbc:postgresql://" + System.getenv("DATABASE_HOST") + ":5432/dbname";
        String username = "postgres"; 
        String password = "postgres";
        String driverClassName = "org.postgresql.Driver";
        /*
         * Create the datasource and return it
         * 
         * You could create the specific DS 
         * implementation (ie: org.postgresql.ds.PGPoolingDataSource) 
         * or ask Spring's DataSourceBuilder to autoconfigure it for you, 
         * whichever works best in your eyes
        */
        return DataSourceBuilder
                .create()
                .url( url )
                .username( username )
                .password( password )
                .driverClassName( driverClassName )
                .build();
    }
}
Just remember that in spring, you can always override allot of the default behaviours with a little bit of digging!
Hope this helps!