Valladolid had taken a half-time lead over Atletico before goals from Angel Correa and Luis Suarez turned the score around. Madrid's late turnaround to beat Villarreal 2-1 was irrelevant due to Atletico's result.
The results mean Diego Simeone's team end the season on 86 points, two ahead of second-placed Madrid and seven above third-placed Barcelona.
It's the eleventh time that Atletico have been crowned champions of Spain, with just three of them coming in the last 40 years, in 1996, 2014 and now 2021.
Atletico have been title favourites for much of the season, leading the league table since December 5 when they went top with a 2-0 win, also over Valladolid.
Key to their early-season success was the form of forward Suarez -- who was deemed surplus to requirements at Barcelona last summer -- who scored 16 goals in his first 17 games.
The role of Marcos Llorente, converted into an attacking midfielder this season by coach Simeone, has also been crucial, bagging 12 goals and 11 assists.
By January 31, a 4-2 victory at Cadiz put Atletico 10 points clear of both Madrid and Barca in the title race.
That was followed by a more challenging spell, as Suarez's goals dried up, and three losses and six draws allowed Atletico's title rivals to begin to close the gap.
Two weeks ago, a rollercoaster matchday 35 saw Atletico drop more points in a 0-0 draw with Barcelona at Camp Nou -- in what looked like a potentially decisive result -- only for Madrid to be held 2-2 by Sevilla a day later.
Last weekend, with all ten matchday 37 games being played simultaneously, Atletico looked to have blown their title chances when they went 1-0 down at home to Osasuna, with Real leading by the same scoreline at Athletic Bilbao.
Two goals in the last ten minutes from Renan Lodi and Suarez turned the race on its head, a 2-1 win setting up Saturday's dramatic league finale.