The service was briefly disrupted by a lone protester against the move to end centuries of all male leadership in the Church.
The bishop, who has worked in the dioceses of Blackburn, York and Chester, said she was "thrilled" at the amount of support she had received since the appointment was announced last month.
Nearly 2000 people attended yesterday's service, which was conducted by the Archbishop of York, Dr John Sentamu.
Speaking after her consecration, the bishop said: "Archbishop Sentamu has observed, 'the way that we show our faith and our love for one another is with two simple things, prayer and parties'.
"Today is an occasion of prayer and of party and I am thrilled that so many want to share in both."
The sole demonstrator, who spoke out to say women bishops were "not in the Bible" was named as "serial protester" Reverend Paul Williamson.
A Church of England spokesman said: "He's got the right to protest but the contrast was between a lone voice protesting and a sea of voices affirming."
