Gene, 30, has been employed in the same role with BMW-powered Williams for the past four years.
The Indian driver said his team aimed to keep up with their rivals who have shown improvement in performance
Dutchman Nicky Pastorelli has been named as a test driver for the Jordan Formula One team.
"I am angered that after a long relationship I should get seven minutes notice that they were pulling out," said Eddie Jordan.
Jaguar team boss Tony Purnell feels the Australian driver is a world champion in the making.
Williams will lose Ralf Schumacher, currently injured, and Juan Pablo Montoya at the end of the season.
Fernando Alonso warned McLaren they were making him look like an amateur.
Susie Wolff made her full test debut with former champions Williams on Friday, the biggest step by a woman driver in Formula One for more than 20 years, with race regulars paying her compliments.
Formula One supremo Bernie Ecclestone has proposed a controversial world championship for women drivers as part of Grand Prix weekends.
Fernando Alonso hopes to extend his Ferrari contract beyond the end of 2016 and reckons he could have 10 more years of racing in Formula One.