The England pair were offered new contracts by the club but have decided to take up new challenges.
Jordan is rejoining Surrey while Salt is switching to Lancashire - the host county for the Manchester Originals in The Hundred, for whom he has been playing in recent weeks.
A Sussex CCC statement said: "We are disappointed to bid farewell to two players that have developed into extremely fine players, represented their country and played in some of the most high-profile leagues around the world during their time at Sussex.
"However, we fully respect their decisions and understand their reasons for moving on to new clubs, where we wish them every success.
"Everyone at Sussex Cricket would like to thank Chris and Phil for their service and contribution both on and off the pitch. We are very proud of them and what they have achieved while wearing the Martlets and will miss their company. We look forward to enjoying their performances for the remainder of the season."
See Sussex CEO Rob Andrew talk about the pair's departures and the upcoming trip to Vitality Blast Finals Day in the video above.
Jordan said: “To be saying goodbye to everyone at Sussex has to be one of the toughest things I’ve had to do to date. In my time at the club I have realised my dream of playing international cricket and I have formed lifetime relationships.
“I now feel it’s time for me to take on a new challenge. I am very proud to have represented such a great club. I want to thank the entire back room staff and my teammates who have been a part of the journey but most importantly the fans and supporters who have made the entire experience extremely special.
“I want to wish everyone at Sussex the best of wishes because the club will always hold a special place in my heart. GOSBTS.”
Salt said: “It will be with mixed emotions that I leave Hove at the end of the season. It has been an incredible journey for me since I first came down to Sussex at 17.
“I’d like to thank my teammates, the entire coaching and backroom staff, the Sussex fans for their brilliant support, and all those who work so hard behind the scenes to make Hove the special place that it is.
“This has not been an easy decision to make. Sussex is a special place to play cricket and I will be forever grateful to the club for giving me an opportunity back in 2013.
“There are too many people to thank over the course of the last eight years, I’ve met some outstanding people and formed lifelong friendships both on and off the pitch and for that I am extremely thankful.
“I wish everyone at Sussex all the best in the future. The club is in good hands with James Kirtley and Ian Salisbury with an exciting group of young players who I hope will bring the club success in years to come.
“Finals Day is going to be a great occasion and hopefully we can put in a performance to make you guys proud and bring the club a trophy. #GOSBTS”