The Executive backed the Scottish National Party's recommendation to appoint Mr Brown, even though Clackmannanshire Council is not part of COSLA.
European minister Jack McConnell sided with the nationalists who had nominated Mr Brown for the position even though COSLA refused to endorse the appointment.
COSLA nominated Angus Council leader Rob Murray as the Nationalist representative for the committee, which consists of eight Scottish councillors, three Welsh and 15 English.
One chief executive said: 'Mr Brown is just not accountable to local government. Mr McConnell has shown a disregard for local government with this appointment.'