Allardyce, 63, took over in October 2017 from Ronald Koeman when the team was sliding towards the relegation zone.
"We have made the decision that, as part of our longer-term plan, we will be appointing a new manager this summer," said club director Denise Barrett-Baxendale.
"On behalf of the chairman and board of directors, I'd like to thank Sam for the job he has done at Everton over the last seven months.
"Sam was brought in at a challenging time last season to provide us with some stability and we are grateful to him for doing that."
The favourite to replace Allardyce is believed to be the former Watford boss Marco Silva.
The 40-year-old Portuguese was the first choice of the Everton owner Farhad Moshiri when Koeman was dismiised.