Barton has had a somewhat controversial career, and played under Allardyce at Newcastle United for under a season. His former manager wished him well on his new venture.
Allardyce said: ''I think he was too young at that time [at Newcastle], he was more concerned about playing [than coaching], but as time has gone on you have seen him evolve into someone who has a big opinion and he wants to put that to the test on how to manage a football club.''
He added: ''I think he is very fortunate he has got that opportunity because there are so many highly-qualified coaches and managers out there and there are only 92 jobs in the league, so it is a very privileged position and he needs to grasp it with both hands and good luck to him.''
The current Everton boss noted: ''It will be nice to see Joey sitting behind the desk. Good luck to him, he has taken on a big challenge. We will see in the next few months whether he can be a manager who progresses through the leagues and moves forward or not.''
Swansea head coach Carlos Carvalhal admitted, that for his part, Barton's divisive character will be a refreshing addition to the world of football managers.
The Portuguese coach said: ''I wish him the best of luck and I will be interested to follow him because he's a very nice and controversial personality. I like this kind of person and if he brings something new and fresh to the competition that is good.''
Carvalhal also warned: ''It is different to be a manager than a footballer. It is a big change and he will understand that after one month. Some ex-players deal with it better than others and I hope he will have a good career.''