There has been no official announcment from the club although the Black Cats management have said that a statement will be made in "due course" on who their new boss will be.
O'Neil had been listed as joint favourite for the job along with former Manchester City and Fulham coach Mark Hughes.
The BBC Sport website reported that O'Neil, whose last mangerial job was with Aston Villa, met Sunderland's owner and chairman Ellis Short on Thursday evening in London to negotiate a deal.
Assistant coach Eric Black will be in charge of Sunderland for Sunday's Premier League match at Wolverhampton with O'Neil taking over after that, the BBC said.
O'Neill, 59, a former Nottingham Forest player, built his managerial reputation at Wycombe Wanderers before successful spells at Leicester City and Celtic.
Source: AFP
Source: AFP