World number 10 Tsonga, who missed the entire North American hard-court season through injury, parted ways with Roger Rasheed at the end of August and has been coachless since.
In an attempt to emulate the recent success of compatriot Richard Gasquet, who has risen to French number one after including two men in his coaching set-up, Tsonga has appointed former world number 17 Escude and former top 100 player Ascione.
“We have begun this project at my suggestion and I am really pleased to begin a new phase of my career with them both,” Tsonga said in Bercy, where he is taking part in the Paris Masters.
“They will be there often, either one or the other depending on the tournament. I like to have different eyes watching what I do.
“I’ve been looking for the ideal situation for some time, and I feel best with them.”
Gasquet, who is on the brink of qualifying for next week's World Tour Finals in London, works with coaching expert Riccardo Piatti and former world number four Sebastien Grosjean.
Since appointing the pair last year, Gasquet has risen from the lower end of the top 20 to world number nine, having not been an established top-10 player since 2008.
Ascione has developed a strong reputation as a coach due to his work with Kristina Mladenovic and Nicholas Mahut, while Escude – a former Davis Cup team-mate of Tsonga’s – has a long-standing rapport with the 28-year-old former world number five.
Because of Ascione’s other commitments, he will not be able to accompany Tsonga to all his events, which is where Escude steps in.
Escude is targeting a maiden Grand Slam for Tsonga, who reached but lost the 2008 Australian Open final, but says success will be measured by Tsonga’s world ranking.
“Of course we will got for all four (Slams), but the important thing for us is to see a rapid movement up the rankings,” Escude said.
“If, after one year, he is still at the same place, we will not have succeeded in our mission.”