برای این کار می توانید از کتابخانه JavaMail API استفاده کنید:
        Properties props = new Properties();
        props.put("mail.smtp.host", "mail.javabyab.com");
        props.put("mail.smtp.port", "25");
        Session session = Session.getInstance(props,
                new javax.mail.Authenticator() {
                    protected PasswordAuthentication getPasswordAuthentication() {
                        return new PasswordAuthentication("username", "password");
                    }
                });
        try {
            Message message = new MimeMessage(session);
            message.setFrom(new InternetAddress("noreply@javabyab.com"));
            message.setRecipients(Message.RecipientType.TO,
                    InternetAddress.parse("to-email@gmail.com"));
            message.setSubject("subject");
            message.setText("email text");
            Transport.send(message);
        } catch (MessagingException e) {
            throw new RuntimeException(e);
        }