Guiseley School was given permission by the south and west plans panel to create the blocks, replacing most of the existing school buildings.
The other would be located centrally on the site off Fieldhead Road, and would include provision for general teaching.
The plans also include removing a 1960s block of classrooms currently on the site.
But some local residents, living on nearby Back Lane, felt the school was too close to their properties, adding rooms in their houses would be visible from 2nd storey classrooms.
One speaker told the meeting: “Firstly I would like to say i am not against the redevelopment of Guiseley School, but it should not be done at the expense of residents on Back Lane
“The building will have a substantial impact on the privacy of our home.
“The block will have views into our children’s bedrooms, living room and gardens. The new teaching block will have an overbearing effect because of the scale of it.
“We believe there is scope to move the building further forward and we would like this to be considered.”
It was suggested by residents that the view from the school’s windows should be obscured, either by steel screening or frosted windows.
Guiseley School headteacher Paul Clayton told the meeting the plans would “maximise learning time”, stating the “excitement among the staff and the students is tangible”.
He added: “It is very important that we start on our planned dates, as this would minimise disruption.
“It’s crucial so our young people can benefit from the type of school that they clearly deserve.”
Commenting on the application, board member Coun Julie Heselwood (Lab) said: “I absolutely agree with the headteacher on the redevelopment, I understand that the government gave agreement for this in 2014, so we really need to move on this.
“The condition of the school is really affecting teaching and learning. We need to get this school rebuilt for the good of the pupils who go there.
“We would never justify spending thousands of public money on screening – that is a ridiculous recommendation. It’s a school – we want natural light coming into classrooms. Putting frosted windows in a classroom is also unacceptable.
“I would urge members of the panel to pass this and let’s get this school built.”
Coun Colin Campbell (Lib Dem) said: “The design of the building is sadly not what I would describe as cutting edge. Had we had a pre-application, there would have been constructive suggestions on the design.
“But we are where we are, and it’s an acceptable design solution, but not a good one.
“It seems to me that a planted solution is do-able. I don’t think these are reasons to hold up the application.”
The plans were put to a vote, which were unanimously accepted. But some found the design itself underwhelming.
Chairing the meeting, Coun Caroline Gruen summed up: “I am disappointed at the quality of designs of recent schools in this programme. We have excellent examples of designs in Leeds, and I am absolutely aware of the urgency of getting this school.
“I do think this programme needs to do more about the design and appearance of these buildings.”