The Education Select Committee, scrutinising the appointment, rejected the choice of Amanda Spielman.
But Mrs Morgan is to override their finding and press ahead with her selection for the independent watchdog.
Mrs Morgan said Ms Spielman "will not shy away from challenging government".
The education secretary said she was "disappointed that the committee underestimated Amanda's vision, focus and leadership style. Her objectivity and openness are important strengths".
Mrs Morgan said she was "100% confident" in her decision - and that "I am not seeking what one committee member described as a 'crusader'."
In a message on Twitter, Ms Spielman said: "I am really pleased that the Secretary of State is confirming my nomination as HMCI today - thank you to everyone who has expressed support."
The ASCL head teachers' union welcomed her appointment - but the National Union of Teachers has criticised the choice of a chief inspector of schools who has never had experience of teaching.
The Liberal Democrats' education spokesman, John Pugh, said Mrs Morgan showed "arrogance and complacency".
The Education Select Committee had taken the unusual step of not accepting the nomination put forward for the next head of Ofsted.
They said that she had failed to show "passion" or an understanding of the "complex role", MPs on the committee said.
But the committee cannot veto the appointment - and Mrs Morgan says that she is going to proceed with her selection for the next head of the education watchdog.
The current Ofsted boss, Sir Michael Wilshaw, steps down at the end of the year.
Amanda Spielman, born in 1961, left Clare College Cambridge in 1982 with an upper-second-class degree in mathematics and law.
She qualified as a chartered accountant in 1985 and went on to work for leading City firms as an accountant, market analyst and investment adviser.
By the late 1990s, she was working for Nomura International, making equity investments worth between Â£250m and Â£500m.
After the birth of her first child in 2001 she focused on part-time study, consultancy and voluntary work.
Her portfolio included:
In 2004, she became research and policy director for the Ark academy chain.
From 2011, she chaired exams regulator Ofqual three days a week, working with then chief executive Glenys Stacey.
She also continued with her consultancy work, giving development advice on public-private education partnerships in Uganda, India and Pakistan for Ark, and as an external reviewer for the TeachFirst education charity, though she has since resigned from these positions.
Last week, Ms Spielman, who is currently chairwoman of the exams regulator Ofqual, appeared before the committee for pre-appointment questioning.
She was grilled by MPs, who were visibly frustrated by her answers on a range of issues on several occasions throughout the hour and 40 minute hearing.
Their report said:
Conservative committee chairman Neil Carmichael said he and his colleagues were "unconvinced" that Ms Spielman was the right person to lead Ofsted, to raise standards and improve the lives of children.
"Ms Spielman's responses on child protection were particularly troubling and did not inspire confidence that she grasped the importance of Ofsted's inspections in preventing children being held at risk through service failure.
"As a committee, we did not leave the session with the view that Amanda Spielman was prepared for the vast scope and complexity of this important role."
He added: "It is unusual for a select committee to find itself unable to support the government's preferred candidate for a public appointment.
"However, it is our responsibility to hold government to account and the seriousness of our concerns regarding this appointment has led us to produce this report to the House of Commons.
"We call on the secretary of state not to proceed with Ms Spielman's appointment."
But on Thursday, Mrs Morgan said: "I chose Amanda Spielman as my preferred candidate for chief inspector of Ofsted because I was impressed by her leadership, and absolute determination to raise standards to ensure every child gets the excellent education they deserve."
She told MPs: "I am sure that Amanda will generate fewer headlines than her predecessor, but I also know that she will not shy away from challenging government, nor offering frank assessments of the performance of our educational institutions.
"I have absolutely no doubt that under her watch Ofsted will play a central - and highly effective - role in supporting and driving improvement in childcare, schools, children's services and adult learning."
Education Secretary Nicky Morgan is to force through the appointment of her nomination for the next head of Ofsted, despite a cross-party committee of MPs saying they had "significant concerns".