McCarthy, who was the Championship's longest-serving manager, having been appointed in 2012, announced last month he would be leaving at the end of the season and the 59-year-old is now the bookmakers' favourite to take over at West Brom.
"We agreed that it was in the best interests for me, the players and the club that I move on now", he said.
The news came following fans' angry reaction to his substitution of Irish teenager Barry Cotter, who had an impressive debut.
McCarthy was the longest-serving manager in the Championship having taken over as Ipswich boss in November 2012.
After the 2-2 draw at Millwall on Easter Monday he admitted a part of him had "died" after his exit was confirmed and that he felt like he was in a driverless auto.
"That was a disgraceful reaction", McCarthy began, "but listen - I won't have to listen to it again because that's my last game".
It has been reported by Stuart Watson of the East Anglian Daily Times and Ipswich Star that he spoke at a conference for three minutes, before saying, "That's my last game, I'm out of here".