Media playback is not supported on this device
In only his third pro contest, 30-year-old Barnes earned a majority points verdict to claim the vacant WBO European flyweight belt.
One judge viewed it as a draw, but the other two had Barnes ahead.
The victory earns Barnes important ranking points as he seeks a shot at a world crown.
Barnes had been a red hot favourite but the contest was much tougher than many had predicted.
In the second round, Barnes was rocked back on his heels by a solid right-hand from his Madrid-based opponent.
Olteanu, a former European champion who fought for a world title, grew in confidence and gave the home fighter plenty to think about.
But Barnes battled to the victory to keep his world title aspirations on track.
One judge saw it as a 95-95 draw, but Barnes was 97-94 and 97-93 up on the other two cards.
"I knew I had won, but it was a very tough fight," said Barnes.
"I am happy to have had the invaluable experience of the 10 rounds and now I can push on."
Barnes won bronze medals at the Olympics in 2008 and 2012 and twice won gold at the Commonwealth Games.
Double Olympic medallist Paddy Barnes has won his professional title by beating Romanian Silviu Olteanu in his home city of Belfast on Saturday night.