The director of Edward Scissorhands and Beetlejuice threw the switch around 21:30 BST after rapper Professor Green played to the crowds.
The free event took place on the promenade at The Headlands Arena in front of the Tower.
Burton, 58, used Blackpool for scenes in his latest film. "Miss Peregrine's Home for Peculiar Children."
"To be given the town's highest honour is incredible and I'm really excited. I'm sure it will be a wonderful show," he said.
The California-born film director achieved fame directing blockbusters including Corpse Bride, Planet of the Apes, Charlie and the Chocolate Factory and Alice in Wonderland.
Describing himself as Blackpool Pleasure Beach's "biggest fan", Burton chose to shoot scenes in Blackpool for The Killers'  music videos Here with Me and Battle Born.
The Illuminations end on 15 November.

Hill, 78, has run every day since 20 December 1964, clocking up 52 years and 39 days.
The athlete, who won marathon gold medals at the European Championships in 1969 and the 1970 Commonwealth Games, has inspired successive generations of runners, whether elite or fun-runners.
Here is how the running community from around England have reacted to the news.
"Best wishes for a speedy recovery to Ron Hill, a true legend.
"He is such a great man and his determination is so inspirational.
"Running every day for 52 years and 39 days is such an amazing achievement.
"His performances in the marathon are also incredible."
"It will be devastating if he has to stop.
"The great thing about Ron is that unlike some people who win gold medals and then pack up he has kept running.
"He's always ready to stop and talk to people.
"For our club his association with us is like Sir Bobby Charlton with Manchester United.
"I once tried to run every day for about five years but I gave up after twisting my ankle on a fell, although I still run quite a lot."
"Ron Hill is a hero to me. I think he is one of the most important figures in the evolution  of running
"I only met Ron once and it was in the early 70s before most runners knew anything about streaks.
"Most running fans know Ron Hill for his great marathon victories and world records, his pioneering exploits that included carbo-loading, wearing mesh singlets, split running shorts. and creating road racing shoes that are as formidable exhibits of his love for running as his incredible streak.
"My streak started May 26,1969 so that's 47 years eight months well behind Ron's 52 years plus.
"I'm going to run as long as I can. The last year was rough due to injuries but I have a couple of dogs who remind me I need to get out there each morning."
"I have never been able to manage a running streak but he has certainly inspired me.
"When times have been tough I have thought about people like Ron.
"I remember the story about how he even managed a run with his foot in a plaster cast.
"If I could still be running in my 80s I would be very pleased."
"Ron Hill is so dedicated and disciplined to his running which shows me what can be achieved and helps me in all aspects of my running.
"I met Ron Hill at the start of the Greater Manchester marathon 2016 had a chat with him and shook his hand and said it was brilliant to actually meet him in person.
"I almost run everyday but as i am training for various distances from 10K to the marathon quite often there are rest days in the schedule.
"He is very much an inspiration - he's been running longer than I have been alive.
"Equalling his record is going to be very difficult
"It is very good for the body to run every day - the problem comes when people try to do too much too quickly.
"It is best to build up slowly and reach a rate that is manageable for you
"Regular exercise is good for your physical and mental health."

Saturday
Premiership
Inverness CT 2-1 Hamilton Academical
Celtic 4-1 St Johnstone
Kilmarnock 0-1 Dundee
Motherwell 0-1 Ross County
Championship
Dumbarton 0-1 Falkirk
Greenock Morton 1-1 Dundee United
Hibernian 1-1 St Mirren
Queen of the South 0-1 Dunfermline Athletic
Raith Rovers 2-1 Ayr United
Sunday's Premiership previews
Partick Thistle v Rangers (12:15)
Hearts v Aberdeen (15:00)
Hollywood director Tim Burton has switched on this year's Blackpool Illuminations.
[NEXT_CONCEPT]
Former Olympian Ron Hill has ended a 52-year streak of running at least one mile every single day after experiencing chest pains.
[NEXT_CONCEPT]
Match reports from Saturday's Scottish Premiership and Championship games.