Moyes replaced Sam Allardyce at the Stadium of Light last month.
Moyes was confirmed as the new Black Cats boss last month after Allardyce departed to manage England.
Sunderland did not hesitate to appoint the former Everton and Manchester United boss, with owner Ellis Short having targeted the Scot on multiple occasions.
In fact, Moyes rejected the chance to take charge last season before Allardyce was appointed.
Some have questioned it given how badly things have gone for him in recent years, but Kirchhoff insists that the club has made a good choice.
“All of us can understand Big Sam for his decision that he wanted to go for the job, nobody can blame him for that,” he told the Chronicle.
“It is ok for us, and we have got a good choice from the club with the new manager. [He] is bringing in some new influence. It is good for us to work with him.”
It now remains to be seen if Moyes can achieve success with Sunderland in the years to come.
It is fair to say that he has a point to prove, with his last two spells with Real Sociedad and Manchester United both ending miserably.
Much will rest on the work that he can do in the summer transfer window, with Papy Djilobodji the only arrival at the club so far but further additions needed if they intend to be more than a team fighting against relegation.