Colombian striker Falcao struck two superb goals, having also hit the winner for Porto in the 2011 final before a big-money move to Spain, and Brazilian Diego snapped up a late third as Simeone triumphed over fellow Argentine Marcelo Bielsa.
Falcao, top scorer in the competition for a second straight season, netted a first-half double to put Atletico in control before Diego, who was suspended for the 2009 final when with Werder Bremen, sealed an emphatic win five minutes from time.
It was a fitting reward for Simeone who has revitalised 2010 Europa League winners Atletico since taking over in late December at the Calderon, where he became a fan favourite as a player in winning a league and cup double in 1996.
The 42-year-old former Argentina captain also lifted the UEFA Cup as a player with Inter Milan in 1998.
"Tonight I am feeling really strong emotions," Simeone said.
"A lot was at stake, people are very fond of me back in Madrid and they really expected this win... I'm really happy to give the fans of Atletico Madrid a new championship as a coach.
"We were very precise, very accurate... we felt comfortable on the pitch. Technically and tactically it was a good match for us."