Actualy, miners are already earning money from transactions fees. Today, miners earn more from receiving newly created bitcoin than from transactions fees, but this will change.

As the number of Bitcoin transactions increases, the reward from transaction fees will also increase. And every time a "halvening" occurs (some call it "halving"), the rewards from newly created bitcoin decreases. For those who don't know, a halvening means that the number of newly created bitcoin with each block will be halfed. Halvenings occur every four years.

So one day the rewards from transactions fees will be bigger than rewards from new bitcoin. And this day is much closer than 2140. By 2140 transaction fees will be more than enough for miners to be happy.