The phrase "he droned on" is correct and can be used in written English.
It is a common expression used to describe someone speaking in a monotonous or boring manner. Example: "He droned on about his day at work, without noticing that everyone else had lost interest in his rambling story."
In one of the few truly awful speeches Clinton gave, he droned on for what seemed hours, eliciting ironic cheers when he finally said "in conclusion... ....... But, as always, he bounced back.
The business bigwigs patiently fixed their eyes on Mr. Mukherjee as he droned on about earmarked funds and infrastructure bonds.
The delegates got so restive as he droned on — the phrase commentators used — that they actually cheered at the words "in closing".
His hired guns in the 2000 race advised him that if he droned on about the environment, he would come across as a tedious tree-hugger.
Would guests be more inclined to listen while he droned on about the European debt crisis, knowing that the presidential liquor cabinet held hope of a promising end to the evening?
Does he drone on, or what?
After they spend the night together, he decides to update the unfortunate woman on his recent history: he drones on for nearly nine pages without interruption.
But he drones on, after all he doesn't know about my condition.
As he drones on through his pet theories, the bar owner turns up the Lil' Wayne on the stereo to drown him out.
He's someone's Home Counties dad, a spluttering retired colonel full of gravy and defeat, spraying little specks of Brussels sprouts from his mouth as he drones on about immigrants at the dinner table, while the kids roll their eyes and push their peas forlornly from one side of the plate to the other.
