Looking at a variety of sources, it seems that Thomas Edison was the first to create vacuum tubes when trying to find better light bulbs in 1883, and was the first to discover the Edison effect where if you heat a conductor and pass charge through it, the charge can jump gaps in a vacuum. J.J Thomson in 1897 was the first to discover and explain how the Edison effect works while working on his experiments on electrons. To prove J.J Thomson right though, current had to flow one way in the tube (and the only way most electronics would have been able to work using the tubes); which is where John Ambrose Fleming invented the Fleming valve in 1904 which forced current to go one way in the tube. The new invention of radios started to be made using vacuum tubes, but they were still unreliable because they were unamplified and passed weak signals. In 1906 Lee De Forest created the Audion tube which had a metal grid on one side that a second current was passed to which acted to control the strength of the current going through the tube, thus being the first triode tube (meaning the outputs were all on, all off, and anywhere between). Later in 1912 Lee came up with the idea of using multiple triode arrays to amplify the signal over all.
sources:
pbs_vacuum_tubes
engineering history
engineering history:diodes
University of Maryland
and the book Father Of The Radio