The pick was the 72nd overall and was supposed to be the first of back-to-back selections.
But the Dolphins ended up trading the 73rd pick to San Diego, moving down five spots and landing a sixth-round pick in the process.
In Vernon, the Dolphins get an undersized defensive end with some pass-rushing ability.
Vernon didn't perform as well as his athletic ability might suggest, as he recorded only nine sacks in three seasons at Miami before entering the draft as an underclassman.
But Vernon was selected more on his potential because he has flashed big-play ability at times.