Murray also won this Wimbledon tuneup in 2009. He is the first Briton to win at Queen's Club at least twice since Francis Gordon Lowe in 1913, '14 and '25.
"It was an unbelievable week for me," the second-seeded Scotsman said. "I started off not playing great but managed to find my way through, and the last two matches were so much fun."
Tsonga was the fifth Frenchman to reach the Queen's final in the Open era. One of others was Nicolas Mahut, who lost to Murray two years ago.
Murray's speed matched by Tsonga's greater willingness to come to the net. Murray earned the only break in the third set, taking a 3-2 lead on his 10th break point when Tsonga sent a forehand wide.
Tsonga, seeded fifth, broke to lead 4-2 in the first set and later saved two break points as he served out the set. Both players had chances in the second set before Murray won the final five points of the tiebreaker.
Murray is now looking forward to Wimbledon, which begins June 20.
"It's been great preparation this week, and I'll work hard the next five or six days to get ready," he said.