He said he chose the name Francis after 12-13th Century St Francis of Assisi, who represented “poverty and peace”.
He urged journalists to get to know the Church with its “virtues and sins” and to share its focus on “truth, goodness and beauty”.
Pope Francis takes over from Benedict XVI, who abdicated last month.
The former Argentine cardinal Jorge Mario Bergoglio, 76, was the surprise choice of cardinals meeting in Rome to choose a new head of the Church.
In his first audience at the Vatican, he said Jesus Christ and not the Pope was the centre of the Church, which he stressed was “spiritual not political” in nature.
He said the Holy Spirit had inspired the resignation of Benedict XVI and guided the cardinals choosing him as the next pontiff.
The Pope said he had been inspired to take the name Francis by a Brazilian colleague who embraced him and whispered “don’t forget the poor” when it was announced that he had been elected Pope.
He said he immediately thought of St Francis of Assisi, the Italian founder of the Franciscan Order who was devoted to the poor.
As well as representing poverty and peace, he said St Francis “loved and looked after” creation – and he noted that humanity was “not having a good relationship with nature at the moment”.
St Francis of Assisi is said to have loved animals as his “brothers and sisters” and even to have preached to birds.