The 22-year-old already had a long-term deal at the club but has extended his contract for another five seasons ahead of Atleti's move to their new stadium, the Wanda Metropolitano.
Saul has long been linked with a move to Barcelona, with Manchester United also reportedly interested in bringing him to the Premier League, but Atleti have been able to persuade the Spain international to commit his future to the club.
"I am very happy because at Atleti we are a family and there is no better place to be," Saul said.
"I will work my full potential on the field as always to pay back the trust that the club is giving to me. I'd like to thank all my team-mates and the coaching staff for their help day by day so that I can be the player I am today."
Saul claimed the Golden Boot for the 2017 UEFA European Under-21 Championship after netting five goals in Spain's run to the final, where they lost 1-0 to Germany.
The midfielder hit a brilliant hat-trick in Spain's 3-1 semi-final win against Italy and Barcelona were put on high alert when he subsequently told reporters he wanted "to earn a bit more money to be able to help out the family".
Atletico moved quickly to tie Saul down to fresh terms to fend off Barca and United and Saul will remain a key player in Diego Simeone's plans for the new LaLiga season.
And sporting director Jose Luis Caminero was delighted to end transfer rumours surrounding Saul by announcing his new deal.
"Saul is an example for all the kids in our academy," Caminero said. "An example of giving, teamwork, solitary on the field and an impressive quality.
"He is an all-around player, with great aerial power, an amazing long distance shooting skill, a tireless worker, a young player with lots of experiences.
"We should feel happy for the agreement we reached because he is such a great player and there are no limits to his growth."