No. 2 Andy Murray def.
Murray will face 2010 Wimbledon runner-up Tomas Berdych on Friday.
Tsonga and Murray are old rivals having met 14 times before, the first of those nearly a decade ago.
Murray, who is bidding to reach a seventh Wimbledon semi-final, revealed he will prepare for Wednesday's last-eight clash by doing yoga and pilates. "To play quarter-finals, it's a good feeling, honestly, because I had some bad days at the start of the season".
"When I hadn't won a Grand Slam it was like, 'This is my chance".
The 21-year-old Australian's attitude was questioned after he lost convincingly to Andy Murray in the fourth round at Wimbledon on Monday.
But Murray will not under-estimate the two-time semi-finalist. I know Tsonga is one of the best grass-court players in the world.
After winning his first four matches in a canter, Murray said the fight against Tsonga had left him battle-hardened for Berdych and possibly a repeat of his 2012 final against Federer.
After losing the second set badly, Tsonga came back in the third. "I'm still alive in this tournament", said Tsonga.
"So everything can happen. I'm also very confident in my capacity to play great tennis and beat players like Andy".
But the conversation about the final won't matter much for Murray and Federer if they can't get through the quarterfinals. However, Milos Raonic holds the only victory of the year, defeating Roger Federer in January during the final at Brisbane.
Milos Raonic sets up a meeting with seven-time Wimbledon champion Roger Federer in the semifinals.
"Goran's done a wonderful job with Marin. He got him to the next level", said third seed Federer, who will be playing in a record-equalling 14th quarter-final at the tournament.
Down two sets to No. 9 seed Marin Cilic, Federer looked cooked in their Wednesday quarterfinal.
Andy Murray is the outright favorite to win at 1.10, while Tsonga is way behind at 7.00. bet365 will be streaming the match live for all punters that want to watch, and they will be offering live in play bets throughout the action. It became so the moment Novak Djokovic's designs on a calendar-year Grand Slam were blown to smithereens by the atomic serves of Sam Querrey.
The influence of John McEnroe, a new addition to his coaching team, was apparent as sixth-seeded Raonic charged into the net behind his booming first serves and confounded American Querrey with a succession of deft winning volleys.
Tsonga played only six games in his last match here when fragile Richard Gasquet's back problems flared up again, but he isn't lacking for court time this week after a marathon against John Isner the round prior to that.
Murray will now play Tomas Berdych in the semi-finals; the Czech beat his French rival Lucas Pouille in straight sets 7-6, 6-3, 6-2 and will meet the Scot in the semi-finals on Thursday in what promises to be a cracker of a contest.
"If I managed to get ahead in the third, I think maybe it could have been a bit different", said Murray.