He had been in charge of the republic since 1983. His current term in office had been due to expire in July.
Under new rules introduced last year, regional leaders are no longer directly elected but are nominated by Russian President Vladimir Putin and then approved by the local legislature.
Putin's envoy to southern Russia, Dmitry Kozak, is due to announce Putin's nominee.
Police said security in the regional capital Makhachkala had been boosted ahead of the session.
Daghestan, which borders Chechnya, has seen a rise in violence blamed on militants and crime gangs.
The Chechnya Conflict
The aftermath of a December 2002 Chechen resistance attack on the main government building in Grozny (epa)