Paul Crossley, 47, underwent months of psychiatric assessment before he was sentenced by a judge to a hospital order until he is deemed fit for prison, where he will spend a minimum of 12 years, the British Transport Police said.
Security camera footage showed Crossley attempted to push a 23-year-old man onto the tracks, unsuccessfully, at Tottenham Court Road station in central London on April 27 last year.
Crossley then traveled a couple of stops to Marble Arch station. There, he shoved an elderly man who suffered multiple pelvis fractures and a severe cut as he plunged head-first onto the tracks.
A member of the public who retrieved him from the tracks also burnt his hand from the electrified rail.
"I didn't get much sleep last night," Crossley later told police.
Detective Inspector Darren Gough, senior investigating officer, said it had been a long and traumatic process for the victims."The physical and emotional impact of such a determined and unprovoked attack really cannot be underestimated," he said.