Simeone penned new terms to 2017 this week.
"I recall speaking to the president back in 2003 when I left as a player. I always wanted to come back here and prepared myself for that," Simeone told reporters.
"I must thank the board for their renewed confidence and absolutely the players who are the architects of where we are today. We can continue on this path, with this commitment and the project that brings us together.
"I also must thank the fans who supported us from day one and put their trust in us, knowing that every weekend we'd share their enthusiasm.
"The club can carry on building what we have been working on for the last 13 months. We have found balance and, from that, stability.
"A club's growth is based on talent, ability, commitment and responsibility of the players, so we can build a better Atletico for the future.
"We will take each game step after step because it is difficult to plan success. If we succeed, we will surely grow because there is strength, energy and ability in all areas of the squad. This fills me with pride."