Mr Clarke will be the London co-ordinator of the newly created British- Mexican Business Network. The appointment was announced after a meeting in London between Mr Blair and Mexican President, Ernesto Zedillo.
Officially Mr Clarke was chosen because of his business contacts with the Latin American state through his directorship of the tobacco giant, BAT.
But coming hard on the heels of the appointment of the Tory former deputy prime minister, Michael Heseltine, to head a new UK-China forum, the selection is likely to be seen as another attempt to stir up Tory in-fighting.
Mr Clarke and Mr Heseltine were a thorn in the side of the Tory leadership throughout last week's party conference with their fierce denunciation of Mr Hague's policy on the single European currency.
Two other leading pro-European Conservative ex-ministers, Lord Garel- Jones and Lord Walker, have also been appointed to the British-Mexican body.
A Tory party spokesman played down Mr Clarke's appointment, saying: "This highlights the paucity of business people in New Labour."