The Uruguayan converted Jordi Alba's low pass in the 22nd minute to give Barca the lead. He then headed in Dani Alves' cross in the 38th before tapping Neymar's pass into an empty net in the 86th.
"We were on top of the table for many weeks and the most consistent team wins the title," coach Luis Enrique told a news conference.
"We will celebrate this, we enjoy our team and the style in which they play. We must value each title win because it is worth a lot."
Suarez finished the season as La Liga's top scorer with 40 goals, breaking Cristiano Ronaldo and Lionel Messi's grip on the honour since 2009.
Barca ended with 91 points, one ahead of Real Madrid who won 2-0 at Deportivo La Coruna.
Ronaldo scored twice for Real to reach 50 goals in all competitions for the sixth consecutive season.
He was substituted at halftime after hurting his foot but there is no suggestion he could miss the Champions League final against Atletico Madrid in two weeks' time.
Goals from Fernando Torres and Antoine Griezmann gave Atletico Madrid a 2-0 win over Celta Vigo while Athletic Bilbao beat Sevilla 3-1.
Atletico finished third on 88 points and Bilbao secured a place in the Europa League by ending up in fifth spot.
With attention on Wednesday's Europa League final against
Liverpool, Sevilla coach Unai Emery put out a heavily-rotated team.
Gerard Pique came close to giving Barca an early lead against Granada when his header was tipped away by goalkeeper Andres Fernandez who also saved well from Messi.
Fernandez was powerless to stop Suarez's opener, however, the Uruguayan tapping the ball home at the far post.
The second goal was delightful. Javier Mascherano launched a long diagonal pass towards the byline and Alves raced to meet it before hooking a cross for Suarez to nod in from close range.
Suarez nearly laid on a third for Neymar but the Brazilian was denied by Fernandez.
Neymar then generously played in Suarez to complete his hat-trick before the end.
HARD WORK
"This title tastes great after so much hard work throughout the year and suffering right until the end," said Barca captain Andres Iniesta.
"The league is the tournament that tests your consistency throughout the year and it's the one we want to win every year."
Real got off to an ideal start at Deportivo when Gareth Bale manoeuvred his way past a defender on the left and cut the ball back to Karim Benzema who squared it for Ronaldo to score in the seventh minute.
The Portugal striker's second in the 25th minute had an element of good fortune, his header from a corner bouncing off Deportivo's Pedro Mosquera on its way into the net.
Ronaldo also hit the post and the crossbar before being replaced by James Rodriguez although there was no suggestion he had an injury two weeks before the Champions League final against Atletico Madrid.
Real ended a campaign that has witnessed upheaval and managerial change by picking up a 12th consecutive league win but their revival came too late to catch Barca.
"We're a little disappointed after the effort we made," said coach Zinedine Zidane. "After 38 league games we can't change the fact Barcelona are champions.
"They deserved to win the league but I take my hat off to my
lads."
(Editing by Tony Jimenez)
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