Terry, who is alleged to have had an affair with the former girlfriend of Wayne Bridge, lost his England captaincy on Friday to Rio Ferdinand following a meeting with national team boss Fabio Capello.
But Ancelotti has backed Terry to continue as captain of the west London club.
Stand by your man: Chelsea fans show their backing for beleaguered Blues skipper John Terry during Sunday's win over Arsenal at Stamford Bridge
Ancelotti said in an interview to Italian newspaper La Repubblica: '(Terry) has maintained the captaincy because it's not my role to monitor the private life of my players, unless this affects their performances.
'For myself and for the club, he is a great captain, a serious professional, a leader and a player who has great closeness to this club, because he grew up in the Chelsea Academy.'
Ancelotti believes Terry's personal situation has not hindered the Blues, who will face Inter Milan in the Champions League knock-out stages later this month.
Come here you: Terry (left) hugs boss Ancelotti
'I guarantee that it has not affected the team in the least,' Ancelotti said. 'We will prepare well for the Champions League.'
When asked what his relationship is like with compatriot and England manager Fabio Capello, Ancelotti said: 'We have spoken and seen each other a few times.'
Former AC Milan coach Ancelotti is enjoying his first season at Chelsea and has no intention of leaving the club, despite reports linking him with the Italy job once Marcello Lippi steps down.
'I will not be there once Lippi leaves,' he said. 'I have a contract with Chelsea.
'I will be a candidate in 2030 when Italy will win the World Cup. I have studied the stats and after the second World War, we have won the World Cup title every 24 years and reached the final every 12 years. Hence, the 2018 final I leave it to someone else.
'Besides, before I leave Chelsea I would like to win the FA Cup, the Premier League and obviously, the Champions League. I am in no hurry. There is a lot of competition here.'
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