The Catalan giants entered the match knowing that a point would be enough to seal the title, but claimed all three in La Coruna to move 11 points ahead of second-placed Atletico Madrid with a game in hand.
Barcelona, who have won La Liga for the 25th time in their history, had to watch Real Madrid land a league and Champions League double last season, but Ernesto Valverde has claimed the title in his first season as head coach.
The result has also mathematically relegated Deportivo from Spain's top flight, with Clarence Seedorf's side now unable to catch 17th-placed Levante in their final three matches of the campaign.
Deportivo boss Seedorf made a couple of changes from the team that started their goalless draw with Leganes last time out. Borja Valle came into an attacking position for the home side, while Michael Krohn-Dehli was also handed a starting role in midfield.
As for Barcelona, Sergi Roberto once again missed out through suspension, while Andres Iniesta was on the bench following the news that the midfielder would be leaving the Catalan giants at the end of the season.
The visitors needed just seven minutes to make the breakthrough on the night, with Philippe Coutinho curling a wonderful effort into the far corner of the net following smart work from Ousmane Dembele inside the Deportivo box.
Deportivo thought that they had levelled in the 17th minute when Lucas Perez smashed home from close range following a smart save from Marc-Andre ter Stegen, but the goal was eventually disallowed for offside.
Borja Valle then fired over the crossbar just before the 30-minute mark as the home side looked to hit back, before Lionel Messi brought a wonderful save from Deportivo goalkeeper Ruben with a curling free kick down the other end of the field.
Deportivo continued to enjoy good moments as Borja Valle just turned wide of the post from close range in the 32nd minute, before Fabian Schar somehow missed the crossbar with a close-range header moments later.
Barcelona were always dangerous, however, and doubled their lead in the 38th minute when Messi's sensational volley from a Luis Suarez cross found the back of the net.
Deportivo answered straight back though, with Perez turning a low Guilherme cross into the bottom corner to give the home supporters something to cheer ahead of the half-time whistle.
Messi had the first chance of the second half following a super pass from Coutinho, but the Argentine turned wide of the post from close range, before Perez tested the reactions of Ter Stegen down the other end of the field.
Samuel Umtiti headed over the Deportivo crossbar just past the hour as Barcelona came close to a third, but it was Deportivo that scored the game's fourth goal in the 64th minute when Emre Colak turned a low Celso Borges cross into the back of the net.
The home supporters were bouncing in the period that followed, and Ter Stegen had to get down to keep out a header from Borja Valle as the pressure continued.
Luis Suarez then struck the side-netting for Barcelona in the 73rd minute, before Guilherme fired over the crossbar down the other end of the field.
Messi almost netted 11 minutes from time when he raced into the Deportivo box, but the Argentine saw his goal-bound strike blocked by two diving defenders, before Ruben kept out a Luis Suarez effort.
Barcelona did regain the lead in the 82nd minute, however, when Messi turned home from close range following a wonderful exchange with Luis Suarez, who picked out his teammate with a sensational pass.
The same two players then combined in the 85th minute as Messi slotted past Ruben to complete his hat-trick. Gerard Pique should have made it 4-2 late on, but the centre-back was denied by a wonderful Ruben save.
Deportivo are returning to the Segunda Division for the first time since the 2013-14 campaign, but they still have matches with Celta Vigo, Villarreal and Valencia to come before the end of the season.
As for Barcelona, Valverde's side have the small matter of El Clasico at home to Real Madrid next weekend.
DEPORTIVO (4-3-3): Ruben; Juanfran, Albentosa, Schar, Luisinho; Borges (Andone 86'), Guilherme (Muntari 83'), Krohn-Dehli; Colak, Lucas, Valle (Fede 86')
BARCELONA (4-3-3): Ter Stegen; Semedo, Pique, Umtiti, Alba; Rakitic (Iniesta 87'), Busquets, Coutinho (Paulinho 74'); Dembele (Denis Suarez 68'), L. Suarez, Messi