He will take over from Rt Rev Stephen Croft who has moved to the Diocese of Oxford.
The appointment of the traditionalist Anglo-Catholic will be of interest to many in the Church due to his views on women priests.
Before being named Bishop of Burnley, he was announced as the successor of Martin Warner as Bishop of Whitby in 2012 but withdrew his acceptance of the role because of a conflict over his strong opposition to the appointment of women as priests and bishops.
Bishop Philip, 50, has held the role of Bishop of Burnley since 2015.
The bishop has extensive experience working in communities with religious, social and economic diversity.
In February 2016, he spoke at General Synod on his hope that the Church of England should 'rediscover' its passion for deprived estates across the country.
Bishop North said he was honoured to be given the opportunity to serve the Diocese of Sheffield.
He said: ""I am both excited and challenged by the prospect of succeeding Bishop Steven who has been a great inspiration to me throughout my own ministry.
"The Diocese has a clear strategy in place for reaching out to those who do not yet know Jesus Christ, and I will enjoy sharing in that and ensuring that all the people in this area know that they can find a warm welcome and answers to their questions in their local Church. I also look forward to finding ways of strengthening our ministry to the poor and the vulnerable and to the young. In a diverse Diocese, I am wholly committed to being a Bishop for everyone and will work to ensure that priests and parishes of all traditions can flourish and find delight in serving God and his people."
The Bishop of Sheffield leads the Church of England in Sheffield, Rotherham, Doncaster and the surrounding areas.
Bishop North will be installed at Sheffield Cathedral in June.