Abbot, who was previously the chief marketing officer for GE's U.S. retail consumer-finance business, will be the CEO of the new venture, Bloomberg News reported.
The group, which also includes T-Mobile, is working with Discover Financial Services (DFS) and Barclays Plc (BSC) to allow people to pay retailers via their phone, rather than using cash or plastic.
Discover's network would process the purchases.
The decision to hire Abbot "should definitely cause MasterCard and Visa to take this initiative very seriously," said Philip Philliou, at payments-industry consulting firm Philliou Selwanes Partners. "You have someone who understands consumer payments, as opposed to this being someone from the telecom industry."