Media reports around England have suggested that ex-Wolves boss Julen Lopetegui will get the job.
Joint-Chairman David Sullivan said: On behalf of everyone at West Ham United, I would like to offer our sincere thanks and gratitude to David for the contribution he has made to the Football Club during his time as manager.
David has been responsible for a period of great progress and success in our history, and we are extremely grateful for all of his hard work, commitment and dedication to the role.
David has been an absolute professional to work with and he will leave with our greatest respect and good wishes he deserves to be held in the highest esteem for the service he has given to West Ham United, and we wish him every success in the future.
By making this announcement now, it allows David to get the send-off he deserves from the West Ham supporters and for us all to show our appreciation to him at our final home fixture of the season against Luton Town on Saturday."
David Moyes said: I have enjoyed four and a half brilliant years at West Ham, and the Club is in a stronger position than when I returned back in 2019.
When I joined West Ham for a second time, the Club was one place above the relegation zone, and it has been a terrific journey to have achieved three consecutive seasons in Europe.
After leading the Club to safety, we guided the team to finishes of 6th and 7th in the Premier League, and I was delighted when we won the Europa Conference League title last June the Club's first major trophy in 43 years.
I would like to thank all the players for their support, and all the success they have achieved, over the last four and a half years.
I have really enjoyed working with everyone at West Ham, and I would like to thank the Board for giving me the opportunity to manage this great Club.
I wish my eventual successor, the Directors, the players, the staff, the fans, and everybody at West Ham, all the very best for the future."