Party bosses had ruled the original annual general meeting invalid and ordered a re-run of the election for office-bearers.
However, Mr Nolan was elected by ten votes to seven, defeating Mike Robb, chairman of the Edinburgh East constituency Labour party, and a front-runner to succeed retiring MP Gavin Strang.
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Hide AdMr Robb denied the result was a setback for his chances, but a party insider described his defeat as "pretty damning".
Mr Nolan declined to comment.