The British veteran, who beat Sweden's Enqvist in last year's final to claim his first Champions Tour event, will next face old foe Goran Ivanisevic at the Royal Albert Hall.
“It’s great to be back in London, the Statoil Masters is such a fantastic event," Henman said. "There’s a lot of amazing buildings and architecture in London and the Royal Albert Hall is very, very special so I always look forward to getting back out there."
Frenchman Fabrice Santoro also got off to a winning start, beating Mark Philippoussis of Australia 7-6(12) 6-3 after claiming an epic first-set tie-break.
Carlos Moya completes the six-man line-up for the Champions Tour event, which runs from December 5 to 9.
In the Legends group, Mats Wilander and Pat Cash met in a thriller, with the seven-times Grand Slam champion Frenchman edging the Australian former Wimbledon winner 4-6 6-3 10-6 in a champions' tie-break.
"At the end of that first set I was nervous believe it or not,” said Wilander. “I choked a bit and then suddenly he had won the first set 6-4. It felt good though.
“I love this court. It's great for serve and volley because the ball stays low with a slice serve and kicks up high with the kick serve so we should see some great tennis this week.
"It's amazing that on a Wednesday afternoon, two 48-year-olds are playing tennis in front of a pretty much packed house in the Royal Albert Hall. That's the beauty of this event and the Royal Albert Hall, it's special."
Ivan Lendl was forced to withdraw from the event after the Czech succumbed to knee and hip injuries. Guy Forget of France will replace Lendl, who currently coaches US Open and Olympic champion Andy Murray.
“I am very disappointed that I will not be fit enough to play in the Statoil Masters Tennis in London,” said Lendl.
“I have been looking forward to playing in the tournament all year having heard so much about it. For now I will concentrate on fixing and rehabilitating my knee and hip but I hope to be able to play at the Royal Albert Hall in the future.”
Also featuring in the Legends draw are John McEnroe, Henri Leconte and Jeremy Bates.
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