Kelly replaces Hanif Lalani who stepped after 14 months in the role.
Former EDS Financial Services head Jean-Louis Bravard, who is now director at sourcing advisory Burnt Oak Partners, says if anyone is capable of turning BTGS around it is Kelly.
"It is an enormous challenge but if somebody can run BTGS it is definitely Jeff Kelly."
Bravard said Kelly's experience running the general motors account at EDS will stand him in good stead. "This is a massive contract that few could run."
It is a massive challenge. BT is restructuring its struggling Global Services business to focus on three separate areas after its "unacceptable performance" led to the group losing more than £1.3bn.
What does the industry think?