Djokovic equaled Roy Emerson's record of six Australian titles and won his 11th Grand Slam championship, moving him into fifth place alongside Bjorn Borg and Rod Laver on the all-time list for most major titles and closing the gap on Roger Federer (17) and Rafael Nadal (14).
"Every Grand Slam title is very significant in its own way," Djokovic said. "Here, because of the fact that I managed to make history tonight and equal Roy Emerson's six Australian Open titles. I'm very honored to be mentioned alongside legends of our sport like Bjorn Borg, Rod Laver, and to win as many Grand Slams as they did.
"I can't lie and say I didn"t think about it. Of course it was in the back of my mind. Coming into the court I knew that I had a chance to make history. Of course it served as a great motivation, as a great imperative to play my best."
The 28-year-old Djokovic, who won three of the four Grand Slam titles in 2015, has a 57-6 record in Melbourne, winning his first major there in 2008.
Djokovic broke No. 2 Murray twice in the opening set, twice again in the second and once in the third. Djokovic only had his serve broken twice.
"It's phenomenal," Djokovic said. "I'm very proud of it, as is my team. We worked very hard to be in this position, and we should enjoy it. We should cherish every moment that we get to experience now because these are the tournaments that we all value, that we all want to play well on. No doubt that I'm playing the best tennis of my life in the past 15 months."
Djokovic improved to a 22-9 record against Murray as he wrapped up victory in two hours and 53 minutes. The Belgrade native won six of their seven meetings last season. Since Murray defeated the Serb in the 2012 U.S. Open final, Djokovic has won 14 of their past 16 matches.
Djokovic paid tribute to Murray in his post-match speech.
"You're a great champion, great friend, a great person who is very professional and committed to this sport," Djokovic said. "So I'm sure in the future you'll have more opportunities to fight for this trophy."
Murray, the 28-year-old Scotsman, paid tribute to his pregnant wife Kim, who is due to have their first child in February and remained in Britain.
"You've been a legend the last two weeks. Thank you so much for all your support," Murray said, choking back tears and waving to the crowd as he walked away from the microphone. "I'll be on the next flight home."
Murray also had to deal with another family matter in Melbourne. Kim's father, Nigel Sears, who traveled to Australia as coach for Ana Ivanovic, became ill and had to be rushed to a nearby hospital by ambulance while Murray was on court in his third-round match. After a night in the hospital, Sears was well enough to return home.
"It"s been a tough few weeks for me away from the court," Murray said.
Murray later told reporters, "I've been held on flights for it feels like five days. The first one out of here, I'm leaving. It's been hard, regardless of today's result. I'm proud I got into this position -- just quite looking forward to get home now."