Office365 only supports the LOGIN SASL on TLS port 587.

To configure your device or application, connect directly to Microsoft 365 or Office 365 using the SMTP AUTH client submission endpoint smtp.office365.com.

Office365 only supports the LOGIN SASL on TLS port 587.

The following code works fine for me when I just tried it (all of these settings can also be set up at design-time as well):

  1. setting the TIdSMTP.AuthType property to satDefault, which uses the SMTP AUTH LOGIN command:

    var
      idSMTP1: TIdSMTP;
    begin
      idSMTP1 := TIdSMTP.Create(nil);
      try
        idSMTP1.IOHandler := TIdSSLIOHandlerSocketOpenSSL.Create(idSMTP1);
        idSMTP1.UseTLS := utUseExplicitTLS;
        TIdSSLIOHandlerSocketOpenSSL(idSMTP1.IOHandler).SSLOptions.Method := sslvSSLv3;
    
        idSMTP1.Host := 'smtp.office365.com';
        idSMTP1.Port := 587;
    
        idSMTP1.AuthType := satDefault;
        idSMTP1.Username := ...;
        idSMTP1.Password := ...;
    
        try
          idSMTP1.Connect;
          try
            idSMTP1.Authenticate;
          finally
            idSMTP1.Disconnect;
          end;
          ShowMessage('OK');
        except
          on E: Exception do
          begin
            ShowMessage(Format('Failed!'#13'[%s] %s', [E.ClassName, E.Message]));
            raise;
          end;
        end;
      finally
        idSMTP1.Free;
      end;
    
  2. setting the TIdSMTP.AuthType property to satSASL and using TIdSASLLogin, which uses the same SMTP AUTH LOGIN command:

    var
      idSMTP1: TIdSMTP;
      idSASLLogin: TIdSASLLogin;
      idUserPassProvider: TIdUserPassProvider;
    begin
      idSMTP1 := TIdSMTP.Create(nil);
      try
        idSMTP1.IOHandler := TIdSSLIOHandlerSocketOpenSSL.Create(idSMTP1);
        idSMTP1.UseTLS := utUseExplicitTLS;
        TIdSSLIOHandlerSocketOpenSSL(idSMTP1.IOHandler).SSLOptions.Method := sslvSSLv3;
    
        idSMTP1.Host := 'smtp.office365.com';
        idSMTP1.Port := 587;
    
        idSASLLogin := TIdSASLLogin.Create(idSMTP1);
        idUserPassProvider := TIdUserPassProvider.Create(idSASLLogin);
    
        idSASLLogin.UserPassProvider := idUserPassProvider;
        idUserPassProvider.Username := ...;
        idUserPassProvider.Password := ...;
    
        idSMTP1.AuthType := satSASL;
        idSMTP1.SASLMechanisms.Add.SASL := idSASLLogin;
    
        try
          idSMTP1.Connect;
          try
            idSMTP1.Authenticate;
          finally
            idSMTP1.Disconnect;
          end;
          ShowMessage('OK');
        except
          on E: Exception do
          begin
            ShowMessage(Format('Failed!'#13'[%s] %s', [E.ClassName, E.Message]));
            raise;
          end;
        end;
      finally
        idSMTP1.Free;
      end;
    

Update: Office365 no longer supports SSL v3, you must use TLS v1.x now:

(idSMTP1.IOHandler).SSLOptions.Method := sslvTLSv1;