“The club is undergoing a period of solid growth and I chose to stay where I am,” Simeone, who had been under contract with the club until 2017, told a news conference on Tuesday.
“I am convinced that the club will continue to grow, I see it getting stronger, I see its enthusiasm,” the 44-year-old added.
Simeone has had a successful spell at the Spanish side since he took charge in December 2011 after Atletico suffered a humiliating King’s Cup loss to third-division side Albacete.
He led Atletico to the 2012 Europa League title before his side beat city rivals Real Madrid in the 2013 King’s Cup final held at Real’s Bernabeu stadium.
Under his watch Atletico won their first La Liga title in 18 years in 2013-14 and narrowly lost to Real Madrid in the Champions League final.
“It is a pleasure to announce the extension of our coach’s contract until 2020. He knows how to take full advantage of the team’s potential,” Atletico Madrid president Enrique Cerezo said.
Simeone is renowned for his ability to think outside of the box, principally in preparing his players for matches.
His message since his arrival at the club has been about teamwork, unity, and humility.
Neither Simeone nor the club gave any contract details but Spanish media said the coach will earn around six million euros ($6.5 million) per season.
In January, Chinese multi-billionaire Wang Jianlin bought a 20 percent stake in Atletico and Simeone has reportedly been told the club will not need to sell their best players to meet huge debt repayments as in the past.
Wang, who is number 42 on Forbes magazine’s list of the world’s richest people with a fortune estimated at $18 billion, will invest a much-needed 45 million euros ($52 million) into the Atletico coffers for his share of the club.
An energetic, hard-tackling midfielder, Simeone left for Europe in 1990.
His first stop was Pisa in Italy and he went on to play for Inter Milan, Sevilla and Atletico Madrid, where he had two spells — 1994-97 and 2003-2005.
Simeone left Europe in 2005 to join Racing Club — the team he supported as a boy — in the Argentine first division.
He retired as a player in 2006 after a spell with Racing Avellaneda, one of several Argentine teams he went on to coach.
He won two Argentinian league titles (Estudiantes 2006, River Plate 2008) as coach before taking over Atletico.
Simeone’s international playing career began in 1988 with a 4-1 defeat by Australia.
He went on to make 106 appearances, played at the 1994, 1998 and 2002 World Cups and was in the teams that won the Copa America in 1991 and 1993.
Simeone gained notoriety at the 1998 World Cup when, feigning injury after a retaliatory kick from David Beckham, he got the England midfielder sent off.
Argentina went on to win the match on penalties after a 2-2 draw.
“You take advantage of all the opportunities you find in your life. If you don’t take advantage of a chance that comes your way you are lost,” he told The Guardian in 2002 when asked about the incident.