Valladolid took a shock lead in the 18th minute when Oscar Plano slotted past Jan Oblak to complete a sweeping counter-attack after Yannick Carrasco had lost control of the ball following an Atletico corner.
Just as they had done in last week's comeback win over Osasuna, Atletico missed a series of clear opportunities but they drew level after a moment of magic from Angel Correa, who danced his way through the defence before arrowing into the bottom corner in the 57th minute.
Suarez then pounced on a giveaway by the Valladolid defence to score in the 67th and put Atletico on their way to a victory that would secure the title no matter what happened in Real Madrid's game at home to Villarreal.
Valladolid missed a couple of glaring opportunities down the other end while Geoffrey Kondogbia wasted a chance that would have given Atletico a more relaxing finish when he blasted into the side-netting.
Real Madrid ended up fighting their way back from a goal down to beat Villarreal 2-1 which meant they would have swiped the title from Atletico's hands if Valladolid had equalised thanks to a better head-to-head record.
However, Diego Simeone's side saw out the victory and wildly celebrated on the pitch.
"Atletico have had an incredible season despite all the difficulties we've had. We've been the most consistent team and we are champions," said Suarez.
Atletico finished top of the standings on 86 points while Real, who snatched a late 2-1 win over Villarreal, came second on 84. Valladolid finished 19th and were relegated to Spain's second division.
Hundreds of fans celebrated in central Madrid after the match, while the police drafted in extra officers and drones to monitor the situation.