The 33-year-old previously held the WBO versions of the super-featherweight and lightweight world titles.
In an all-action performance, Burns floored 34-year-old Di Rocco in the eighth round, and although the Italian rose to his feet, referee Terry O'Connor waved off the contest.
Burns became the first ever Scot to win world titles at three different weights.
Di Rocco was down in the third round and given a standing eight count having already had a time-out for a low blow earlier in the round.
Burns's aggression was paying dividends against an opponent who appeared somewhat taken aback.
Di Rocco started to pick things up from the sixth round but he was in trouble several times in the eighth before he was knocked down by a right hand.
That proved the end for Di Rocco but a new beginning for Burns, who had lost three of his previous six bouts.
Burns beat Puerto Rican Roman Martinez to win the super-featherweight title in 2010, defending it three times.
He won the lightweight title in 2011, beating Australia's Michael Katsidis but after successfully defending it four times, he was well beaten on points by American Terrence Crawford in 2014.