They are called clip-on tri bars or clip-on aero bars.
There are several things you might want to consider before buying some though.
1) They are designed to fit normal road bars and over-size road bars. Your flat bar may have a different diameter (you can get round this with shims but you would have to make/source these seperatelly)
2) The reason TT and Tri users use this possition is for a more aerodynamic possition, these bars arent the only difference between their bikes and normal road bikes, the whole geometry is different, they have steeper seat tubes, shorter top tubes and the forks have more rake (to maintain stability with weight shifted forward). When fitting these bars to a road bike without modification, typically they will close your hip angle and drop your power output and de-stabilise the bike to some degree making it twitchy. So you will need to try to find a bar that maintains your hip angle, something more like audaxers use rather than triathletes and time triallists. Or you can modify your bike fit by lowering your bars and pushing saddle forward and up. But this will compromise your normal riding possition. Also if you plant to ride in traffic on them, think again, they are made for going in straight lines at high speed, not weaving about in traffic.