Diego Simeone's side lifted the title for the first time since 1996 thanks to the defender's second-half equaliser
Injuries to Diego Costa (hamstring) and Arda Turan (pelvis) inside the first 25 minutes looked to have damaged Atletico's hopes and Alexis Sanchez's stunning 34th-minute goal gave Barcelona all the momentum.
But sloppy marking from a corner would ultimately cost the hosts, who allowed Godin to steal in unmarked and head in the all-important equaliser four minutes into the second half.
Lionel Messi had a goal ruled out for offside as the hosts sought a response, but they were ultimately denied by the visitors' typically stubborn defence, as Atleti clinched the title by three points.
The title is Atletico's 10th in the Spanish top flight and ensures they finish the season unbeaten in all six matches they have played against Barcelona.
And, although Costa and Turan's injuries will reduce their chances of winning next week's Champions League final against bitter rivals Real Madrid, Atletico will first be celebrating the end to their 18-year Liga drought.
Simeone's men led the league by as much as six points in April but stuttered in the run-in, only to produce when it counted in Barcelona, who may have played their last match for under-pressure coach Gerardo Martino.
Passed fit to play despite pre-match doubts, Costa started alongside ex-Barcelona forward David Villa, while the hosts - who surprisingly left out Xavi - recalled Gerard Pique after he recovered from a hip injury sustained against the same opponents last month.
Any suggestions that Atletico would play for a draw were quashed in the early stages, as Miranda nodded a free-kick wide before Juanfran's dangerous ball into the penalty area had to be cleared by Pique.
But disaster struck for the visitors in the 14th minute as Costa pulled up clutching his hamstring and was forced off.
The striker, who has scored 36 goals in 51 appearances this season, could not control his emotions as he broke down in tears on the bench. He would be joined by Turan nine minutes later when he failed to recover from a pelvic injury sustained in a collision with Cesc Fabregas.
Atletico's double-blow gave Barcelona a boost and after a cagey start they began to create chances as Alexis and Pedro failed to convert headers after excellent crosses from Dani Alves on the right.
Pedro's failure to hit the target from a free header was particularly disappointing, but Alexis sent the partisan crowd wild in the 34th minute with his outstanding finish from just inside the area.
Messi chested down a lobbed Fabregas ball and Alexis pounced, thrashing a half-volley past Atletico goalkeeper Thibaut Courtois and into the top-right corner from an incredibly difficult angle.
Tempers frayed before half-time, with four players booked in the 10 minutes before the break and Atletico came out breathing fire once play resumed.
Villa was the first to go close, firing a left-foot volley into the post after beating Barcelona goalkeeper Jose Pinto with a quick shot on the turn.
The forward was then played in, but under pressure from Alves could not get a shot off before the onrushing Pinto cleared.
Atletico did get their goal four minutes into the second half though, as the unmarked Godin made the most of Barca's flat-footed defence to score a towering header from Gabi's corner.
Neymar made his first appearance in more than a month from the bench as Martino chased the game and, in the 63rd minute, Barcelona thought they had taken the lead.
Messi was the man to fire home an instinctive volley - which flew into the roof of the net from close range - only for his effort to be adjudged offside.
Alves had a fierce strike tipped over in the latter stages, but despite their late pressure, Atletico clung on and were applauded for their efforts by the Camp Nou faithful at full-time amid wild celebrations from the small contingent of away supporters.