There is still some negotiating to be done regarding a six-figure compensation fee due to the Irish Football Association, but O'Neill has agreed in principle to a four-year contract at Stoke.
The Potters turned to O'Neill after being rebuffed in their efforts to appoint Preston North End manager Alex Neil, following the sacking of Nathan Jones.
They sit bottom of the Championship and have picked up just eight points from 15 games.
O'Neill, who will double his £750,000-a-year salary at the Bet365 Stadium, is set to be joined by Northern Ireland head scout Andy Cousins.
Speaking at Wednesday's squad announcement in Belfast, O'Neill was asked about potential interest from Stoke.
"It is always flattering".
O'Neill has been Northern Ireland manager for over seven years and guided his team to the Euro 2016 finals, where they would progress to the knock-out stages.
The former Newcastle midfielder has been interested in a return to club management for some time and was linked with the Sunderland job in 2017 before turning down an approach from Scotland past year.
After that, they were denied a World Cup finals spot only by a highly contentious play-off defeat to Switzerland and are now highly likely to feature in the Euro 2020 play-offs in March.