Agassi, 32, recorded a 6-2, 6-2, 6-1 victory that made him the first non-Australian to win this tournament four times. He moved into a tie for sixth place on the all-time Grand Slam victory list, drawing even with Ivan Lendl, Jimmy Connors, Ken Rosewall and Fred Perry.
He needs two more Grand Slam championships to tie Bill Tilden for fifth place.
It was the 21st straight Australian Open match won by Agassi, more than any player in history. He won the title in 2000 and 2001 before withdrawing from last year's event with a wrist injury. He also won the tournament in 1995.
Schuettler, appearing in his first Grand Slam final, was overmatched from the start. He did not win a point in either of the first two games and was broken eight times.
His hopes of staying in the match came crashing down in the middle portion of the second set. With that set still on serve in the fourth game, Schuettler won the first two points on Agassi's serve.
But Agassi then ran off four straight points to hold serve, after which Schuettler slammed his racket to the court in disgust. He followed that up by losing the first three points on his own serve and was eventually broken.
Schuettler then battled back to win the first two points on Agassi's serve again, only to lose four points in a row once more to fall behind, 4-2. The German held serve only once more for the remainder of the match.
"There is not a single day that is guranteed or promised to you," Agassi told the sellout crowd of 15,000 at Rod Laver Arena in accepting the championship trophy. "Days like this are very rare. You never know when it will be your last win.
"I'll never forget being here and I'll never forget the love I have always felt coming down here. I feel like I am half Australian. I'll come back and work as hard for you as long as I can, I promise."
Agassi has said that his wife, retired superstar Steffi Graf, would play mixed doubles with him at the French Open later this season if he won the Australian Open.
Schuettler made reference to that when he was introduced in the post-match ceremony.
"There is not a lot to say. I tried my best, but Andre was too good for me today," he said. "I think everybody now is looking forward to the French Open."
Agassi dropped just one set and lost only 48 games in his seven matches during the past two weeks. The one lost set came against Frenchman Nicolas Escude in the fourth round.
It was the 14th Grand Slam final for Agassi.
Schuettler became only the second German in the event's 98-year history to advance to the men's championship match. He did so with a 7-5, 2-6, 6-3, 6-3 victory over ninth-seeded Andy Roddick.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys