A total of 240 children were signed up to Rep's Children and were able to see special annual performances by Birmingham Repertory Theatre.
The theatre said all 400 babies born at Birmingham City and Sandwell hospitals in October 2004 were invited to join.
The babies saw their first performance, Open House, aged just six months.
It included actors singing the nursery rhyme Twinkle Twinkle Little Star and interactive play.
Other shows included Dreams Come Out to Play, which was performed in a tent on the main stage, and Princess and Ginger, which the Rep's Children helped create.
The project was funded by the city council, Sure Start, Heart of Birmingham PCT and the Baring Foundation.
A second Rep's Children project begun in 2013, as part of the theatre's centenary celebrations.
Alison Fuller, whose daughter Amaya was born on 1 October, 2004 and was among the first to join Rep's Children, said it had been an "absolute privilege" to take part.
"The Rep's vision was so forward thinking and in my humble opinion I believe the project has achieved what it set out to do, making the theatre accessible for all, regardless of race, culture or social status," she said.
MS Fuller said it had a "positive effect" on her family, including her three older children who have pursued paths in drama and theatre production.
Steve Ball, associate director at The Rep, said staff had enjoyed the experience and hoped the children would continue to see shows at the theatre.
"It's also been an amazing creative challenge for us to develop high quality and engaging live theatre for babies, toddlers and school-age children.
"When we started there were very few productions available to appeal to babies and toddlers, so we had to create it from scratch."
A decade-long project to allow children from some of Birmingham's most deprived areas to see free theatre for their first 10 years has come to a close.