Barca secured their 25th title with the win, having been unbeaten up until now in league games.
Barcelona have now incredibly finished top in seven of the past 10 La Liga seasons, while Deportivo have been relegated to the Segunda Division following today's result.
Valencia's march towards Champions League qualification was delayed after they were held to a goalless draw at home to Eibar.
"Ernesto Valverde's side confirmed their unquestionable superiority in a competition they have dominated from start to finish", Marca said.
"It's terribly hard to think of all the tests we have to go through, to do it with four games going is a great achievement".
The only blemish on their season was a stunning Champions League quarter-final loss to Roma when they blew a 4-1 first-leg lead to be dumped out at the Stadio Olimpico.
In the English Premier League, it is very common, however, in La Liga, it is a controversial issue.
Barca finally saw off their stubborn hosts, though, as Messi pounced after a brilliant one-two with Luis Suarez before slotting in to complete his 30th La Liga treble.
The visitors found themselves under a little more under pressure than they would have anticipated in the opening stages, with Depor leaving their respects to the guard of honour they offered ahead of the first whistle.
"We have not lost a lot of matches, just one in the Copa del Rey and unfortunately one in the Champions League". In all my career, I tried to be a good sportsman, a good person, being respectful.
When asked what Lopez's secret was following Friday's win at home to Sevilla, Morales said it was simple, "he told us to go out and enjoy ourselves". "It was unexpected. It's hard to do what we have done [domestically], but as we want to win everything, there's always a but".
Lionel Messi was at his sublime best at the Riazor as his goals matched with a Philippe Coutinho strike, not only ensured the league title but also relegation for their opponents.