His sudden arrival didn't give his parents Asia and Ronan time to make it to the hospital.
Mr Smith said they had never planned on a home birth, but it was a wonderful experience.
"It's a story I'll never get tired of telling," the second-time father told the Herald.
The couple already have a daughter, Sophie (18 months).
Last Friday morning, Mrs Smith got the first indication that her second baby was on the way.
Six hours later at the maternity unit of Galway University Hospital nothing had happened and they asked if they could go home.
"Asia was feeling cramps later that evening, but she didn't think her contractions had started.
"Then, at 10.30pm, her waters broke and we knew we had to go."
But things happened quickly after that. Mr Smith rang the hospital on his phone while his wife contacted the ambulance. In the panic of talking to the ambulance crew, I cut off the hospital," he recalled.
"A paramedic asked me if the baby had crowned and I'd say within the next two or three seconds he just dropped into my arms."
The ambulance crew told him to encourage the baby to cry and about 30 tense seconds followed before little Jakub made his first sounds.
"I felt a bit calmer then. I knew we were over the worst," he added.
Mother and baby were taken into hospital where they were monitored until staff at the maternity unit were sure everything was all right.
The happy arrival was the second bit of good fortune for the family. This week Mr Smith, who had been unemployed, started a new job as a care worker with the Brothers of Charity in Clarinbridge.