And youngsters are delighted with their new facilities with its 15 classrooms and state-of-the-art information and communication technology suite.
Headteacher Margaret Gordon and her staff were given a few extra days after the summer holidays to prepare the school for opening.
She said: "The pupils absolutely love their new school. On Friday we had an assembly and asked for their favourite part of the school.
"One of the youngsters shouted out, 'Miss, this is a five-star school'.
"We've also been giving tours to parents and the immediate response has been 'wow'. They just can't believe how impressive it is."
Based in the former Dowanhill Primary School, the school includes Notre Dame, St Peter's and Anderson Street Nursery, which has been renamed Elie Street Nursery.
It retains the old Victorian building, which is C listed, but has been extensively upgraded and a new extension built.
The school houses 15 classrooms, two general purpose rooms, a games hall, a library and ICT suite, an assembly and dining hall, a games area and nursery playrooms.
Notre Dame now has capacity for 434 pupils with 60 children able to attend the nursery.
Mrs Gordon added: "We have to thank City Building who bent over backwards to make sure the school was opened in time for us.
"It's absolutely amazing what they have managed to achieve with the old building - it's been flooded with light and looks fabulous.
"I was head teacher of Notre Dame for 11 years and it's an absolute joy to have the privilege of opening this new-build at this stage in my career. The assembly was emotional for me."
Built in 1894, the listed building has had new perimeter railings and gates installed; new landscaped playgrounds and gardens; a new bridge connection to adjacent Dowanhill Park and the existing road has been turned into a car park.
Designers wanted to keep the best elements of the original building and create new features that would enhance the surrounding neighbourhood.
It was also important that the new-build would still be a West End landmark and a sustainable asset for the community.
The design process began in 2010 with building taking place between January 2012 and August this year.
Staff worked hard to make sure the two primary schools blended together effectively.
Pupils were given tours of each others' schools and had joint sports days and discos as well as a special Roald Dahl-themed day.
St Peter's has been acknowledged in the new school crest with the keys of St Peter added to the existing Notre Dame badge.
The school is also working to create a heritage exhibition with stories and artefacts from the two schools.
Councillor Stephen Curran, executive member for education and young people, said: "It's exciting times for the pupils starting the new school term in new premises.
"I'm sure everyone will be delighted with their new school and nursery facilities.
"The children and staff can look forward to enjoying the benefits of a school building fit for the 21st century and I wish them every success in the years to come."