They added: “Results and performances over the course of the second half of last season and the start of the 2025-26 season have not matched expectations.”
In a statement via the League Managers Association, Potter said: “I am incredibly disappointed to be leaving West Ham, particularly without being able to achieve what we set out to achieve at the start of our journey in East London.
“I do, however, fully acknowledge that the results have just not been good enough up to now.”
Potter, 50, had been preparing for Monday’s game and fulfilled his media duties on Friday, saying he believed he had the board’s backing after “positive talks”.
After last Saturday’s home defeat by Crystal Palace, BBC Sport reported that West Ham were considering managerial alternatives, and discussions with Nuno have accelerated over the past 72 hours.
Nuno, 51, was sacked after 21 months in charge at Forest – and only three games into this season.
Last term the Portuguese guided them to seventh in the table – their highest finish since 1994-95 – as they qualified for Europe for the first time in three decades.
Potter took charge of 25 West Ham matches after being appointed in January – winning six – and they finished 14th last season.
“The board would like to thank Graham and his coaching staff for their hard work during their time with the Hammers and wish them every success for the future,” West Ham said.
“The process of appointing a replacement is under way. The club will be making no further comment at this time.”
Former Wales captain Ashley Williams told BBC’s Football Focus: “For the West Ham fans and the club, they want to see a hard-working team and a bit more bravery in possession.
“Under Potter, it was flat – there was nothing for the fans to get behind. Nuno can galvanise the club and he is the perfect person of the available managers to put in there.
“West Ham have been so easy to play against. You only have to get out of second gear to beat them.
“Nuno will organise his team and figure out what players he wants and what players he can work with.”