The 35-year-old, who has cerebral palsy, won the seat from the former deputy prime minster Nick Clegg in what proved one of the most high-profile casualties of the election.
Mr O'Mara will become the fifth disabled MP in the House of Commons after he was voted in to government along with Marsha de Cordova in Battersea.
During his acceptance speech, the new Labour MP made no bones about his disability and revealed it had not stopped him achieving his dreams.
He said: "Twenty years ago there was a fifteen-year-old boy with cerebal palsy who went to his careers advisor at school.
"His careers advisors asked him “What would you like to be when you grow up?” And that fifteen-year-old boy with cerebal palsy said “I’d like to be a politican.”
"If you haven’t noticed already, that boy is me."
Mr O'Mara, who was born in Sheffield, was born with cerebral palsy hemiparesis, making the right side of his body considerably weaker than his left.
Despite problems with tiredness and fatigue caused by his disability during campaigning, Mr O'Mara inspired almost 22,000 voters to choose him to represent Sheffield Hallam.
Following his triumph, Mr O'Mara paid tribute to his campaign team and former Lib Dem leader Nick Clegg. However, he had a special message to his new constituents.
He said: "I do have cerebal palsy and I want every single disabled person out there to know, everybody who’s got learning difficulties, everyone who has mental health issues, everybody who has a physical disability like me, or has any illness…
"I will be on your side. I will be your ally and friend and champion in Westminster.
"Let’s all go on this journey together guys."