Jaylen Brown found Derrick White to score a decisive three-pointer with 45 seconds left to play and seal a 105-102 win for the Celtics.
It is the second time in three seasons they have reached the NBA Finals.
“It’s been nothing but a grind, we haven’t skipped any steps all season,” said Brown.
“We’ve got a bunch of great guys in this locker room, tough guys. Our coaching staff has been great, front office great and now we want to take the next step.”
Brown scored 29 points while Jayson Tatum added 26 points, 13 rebounds and eight assists as the Celtics ran out 4-0 series winners.
“Look at all the talent, look at the players we have,” said Celtics head coach Joe Mazzulla.
“It’s really all about them, they let us coach them. They allow us to push them, they listen to us and they set the temperature of the organisation every single day.
“As a coach, the greatest gift you can have is a group of guys that trust you and allow you to coach them.”
Boston, who will feature in the NBA Finals for the 23rd time in franchise history, have raced through their post-season fixtures, beating the Miami Heat, the Cleveland Cavaliers and the Pacers with a 12-2 record.
They will face either the Dallas Mavericks or the Minnesota Timberwolves in the Finals.
Dallas lead 3-0 in the best-of-seven series as they prepare to host Minnesota in game four at 01:30 BST on Wednesday.
