I think it works very much like job promotion does nowadays. He obviously had the skill set, but the only assignment available to him was Transportor Chief, especially because he was a non-com. He was probably able to get the DS9 gig because it was run down and in the middle of nowhere, so there wasn't much competition. I'm guessing having experience with Cardassians would also be benefit to him landing the job.
Or it could just be that TPTB wanted a familiar face on DS9 so viola! O'Brien is an engineer.
Heck, where did Geordi get his Enginering skills? Remember, he started out flying the ship like Sulu.