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New Zealander Cotter, who was in charge of Scotland's national team from 2014-17 and spent more than a decade coaching in France, took over from John McKee as Fiji coach after last year's Rugby World Cup.
He overhauled the coaching staff, bringing in former international referee Jackson as a skills coach.
Jackson, who spent nine years as a referee after a long professional playing career in New Zealand and England, would also help teach the players how to deal with officials.
"This will help us a lot because if we can cut down the discipline and the penalties against us, it will make us less vulnerable," Cotter said in a Fiji Rugby Union statement.
Former All Blacks midfielder Gibson, who was in charge of the New South Wales Waratahs from 2016-19, will be backs coach, while Gray, who worked with Cotter in Scotland and France, has a specific role around the breakdown.
Fiji will play France on Nov. 15, Italy on Nov. 21, Scotland on Nov. 28 and a final game the following week against England, Wales, Ireland or Georgia.
The matches have been organised after COVID-19 restrictions prevented southern hemisphere teams going on their usual end-of-season tours of Europe.
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)