Akindele, a Peoples Democratic Party (PDP) representing Okitipupa, was removed over alleged fraud.
Fatai Olotu, the deputy speaker representing Akoko north, was also removed.
Their removal was carried out by 15 members of the PDP and five members of the All Progressives Congress (APC).
Malachi Coker, a lawmaker representing Ilaje 1, was subsequently elected as acting speaker while Ayodele Arowele was elected his deputy.
Akindele and Olotu were first impeached by 18 out of the 26 members for alleged highhandedness in 2016.
They were saved by the intervention of Olusegun Mimiko, outgoing governor of the state.
Their sack comes less than a month to the inauguration of Rotimi Akeredolu as the new governor.