Here's a demo of 2 ways to add GeoJSON to a Leaflet web map: http://codepen.io/pmckinney/pen/mELyNY
I know there is also the Leaflet-AJAX plugin.
And if you're interested in converting a shapefile or feature class to GeoJSON, check out the City of Philadelphia's ArcToolbox.
Does anyone know why the output of the ArcGIS Desktop JSON conversion tool does not work in Leaflet? I've always wondered what was going on with this.