the first Grand Slam title by any British man since Fred Perry won the 1936 US championship and Murray's first in five Grand Slam finals trips.
"He deserved to win this Grand Slam more than anybody because over the years he has been a top player, he has been so close, lost four finals," Djokovic said.
"Now he has won it so I would like to congratulate him. Definitely happy that he won it."
Djokovic, World No. 1 Roger Federer and Spain's Rafael Nadal had won 29 of the prior 30 Grand Slam titles with Murray the only rival who had consistently challenged the top trio and repeatedly reached Slam finals.
"Us four, we are taking this game to another level," Djokovic said. "It's really nice to be part of such a strong men's tennis era.
"There's no doubt he deserves to win a Grand Slam, playing so consistently well and winning against the top players for many times on many surfaces.
"He has proven today that he's a champ and he deserves to be where he is, no question about it."
Murray credits his struggles against five-time Grand Slam winner Djokovic, 11-time Grand Slam winner Nadal and 17-time Grand Slam champion Federer with making him into a champion and maximizing his potential as a tennis player.
"Playing against them has made me improve so much," Murray said.
"Maybe if I had played in another era I might have won more but I might not be as good a tennis player."
Until Monday, Murray had managed to take only one set in losing to Federer at the 2008 US Open, 2010 Australian Open and two months ago at Wimbledon as well as to Djokovic in the 2011 Australian Open final.
After an emotional loss at Wimbledon, Murray battled back last month on the same All England grass to defeat Federer for the Olympic gold medal, a boost of confidence that helped carry him to his Grand Slam breakthrough.
"It was just a matter of belief, really mentally to mature and to understand what you need to do to become a Grand Slam champion and to become the best in the world," Djokovic said.
"Andy has all the capacity he needs, all the talent on the court. He's dedicated. He's professional. He has proven that many years already with his results.
"Obviously the last couple of years, it was a necessary experience for him also to understand what he needs to do to be in the position that he is today.
"He has done it."
Murray, 25, had to battle for his crown, winning the first two tight sets before dropping the next two and fighting back in the fifth for the victory.
Not since John McEnroe beat Bjorn Borg for the 1980 US Open title had any player won the first two sets, then dropped the next two only to take the final.
"Andy winning tonight makes it even more competitive and more interesting for people to watch," Djokovic said.
"It's obvious that the four of us, we get to the later stages of every single Grand Slam. It's a privilege to be part of this era."