The duo, who both spent stints out on loan this season with Leeds United and Nottingham Forest respectively, will be leaving The Hawthorns as Steve Clarke trims his squad
The Baggies decided against offering Thomas, who has struggled to cement a place in the first team, a new deal and opted against activating the one-year extension written into Jara's contract.
"Both Jerome and Gonzalo have played important roles in helping the club reach and stay in the Premier League since joining us four years ago," Sporting & Technical Director Richard Garlick told the club's official website.
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Steven Reid, Zoltan Gera and Marc-Antoine Fortune are also out of contract in the summer but the club are still in negotiations with the trio, with the Baggies especially eager to extend Reid's stay.
"Steven's an important figure both on and off the field and we are in negotiations with him regarding a new deal," Garlick continued.
"Zoltan's situation is a little different in that he is rehabilitating from a serious injury. We plan to hold talks with him later this summer and he will continue to have our full support in his efforts to regain full fitness.
"We have not offered Marc-Antoine a new deal at this stage but he remains under consideration as we weigh up all the options for next season."
West Brom enjoyed their best-ever Premier League campaign, finishing in eighth place, and they were helped by several astute loan signings.
The most notable loanee was Romelu Lukaku, who scored 17 league goals for the Baggies, and Garlick remained coy on whether the Belgium international would return to the Hawthorns next season.
"Romelu deserves all the credit he has been getting for his fantastic contribution," Garlick added.
"He will report back to Chelsea pre-season, as planned, and it will be down to them whether Romelu is made available for loan again, and to whom, next season.
"Goran [Popov's] loan has also come to an end and we plan to hold talks with Dynamo Kiev in the coming weeks to decide his future. Yasinne [El Ghanassy] leaves us with our best wishes."