The think tank will include FA chairman Greg Dyke, former England manager Glenn Hoddle, plus Football League chairman Greg Clarke and FA vice-chairman Roger Burden.
League Managers' Association chairman Howard Wilkinson also features, along with new Professional Football Association chairman Ritchie Humphreys, Crewe director of football Dario Gradi and ex-England defender Danny Mills.
Lineker indicated on Friday he believes Dyke has made poor appointments.
Match of the Day presenter Lineker said on Twitter: "No wonder they announced Glenn Hoddle early on @FA commission. Most of the others are utterly pointless. Expected better from Greg Dyke."