Up to now, Rt Rev North's been the Team Rector of Old St Pancras parish in north London. He takes over from the Rt Rev John Goddard, who retired in July.
The Archbishop of York, Dr John Sentamu, is leading the service. He did not lay hands on Rt Rev North, because of the Bishop of Burnley's opposition to female bishops.
Most Revd Dr Sentamu previously laid hands on the first woman bishop, the Bishop of Stockport Rt Rev Libby Lane, last week.
Dr Sentamu said: "I met with the Rev. North to discuss with him how his consecration would be handled given his theological convictions about the consecration of women to the episcopate.
"The Rev. North is not the sort of priest who would insist on a particular set of arrangements for his consecration and any suggestions to the contrary are mistaken."
"These arrangements are for prayer, not politics."
Some have referred to the Archbishop of York's decision as the "theology of taint" - that someone who lays hands on a woman to ordain is then "tainted".
Mr Sentamu says his decision not to lay hands on Rt Revd North was nothing to do with this.
At the time of his initial appointment as Bishop, Rt Rev North said: "It is a great pleasure to be here and a daunting privilege to be appointed Bishop of Burnley.
"I am very excited about sharing in the ministry of the church and the life of the community in this region.
"... inter-faith work is something I am very familiar with where I am currently based in London. I am a governor of a church school with a 68% Muslim population and I have sought to encourage close links between people of all faiths to strengthen the already vibrant local community.
"One of my great passions is work with young people, and here there is so much to build on, not least with the Diocese's fantastic network of church schools."
Rt Rev North was forced to withdraw from a previous appointment as a bishop when parishioners disagreed with his views on female bishops.