If Comedy Central was determined to promote from within, he's probably one of the only ones that would make sense when you take out everyone that is either leaving (Bee, Jones), busy with other projects (Madrigal, Mandvi, Schaal), wouldn't fit the style of the show (Black, Hodgman), or doesn't want the job (Williams). After that, you're left with Noah, Klepper, and Minhaj.
Still, it's a little baffling to give the show to someone that's only had three appearances. Look at how long it took for Colbert, Oliver, and Wilmore to get their own shows. Trevor Noah was a recent enough addition to the show that I suspect they might've picked him up with this idea in mind though. Really, considering how few veterans there were to choose from, I suppose they were going to have to go with someone relatively untested, but at least Noah has several months to try to hone his skills before Jon Stewart steps down.