Свифт 3 версии ответа @Alexey Globchastyy:
class func getGenres(completionHandler: @escaping (genres: NSArray) -> ()) {
...
let task = session.dataTask(with:url) {
data, response, error in
...
resultsArray = results
completionHandler(genres: resultsArray)
}
...
task.resume()
}