The club said that the roles for the rest of the backroom staff, including manager Nigel Pearson, will not change as a result of Robinson's appointment.
"The appointment of Terry Robinson will add another dimension to the club and to our football operations," CEO Susan Whelan said.
"The appointment of Terry will complement the wealth of football experience already in place in our manager, Nigel Pearson; academy director, Jon Rudkin and football operations director, Andrew Neville, whose roles all remain unchanged.
"I would like to take this opportunity to welcome Terry to Leicester City and wish him great success in his new role."
Robinson has previously been chairman at both Bury and Sheffield United.