With over 60s eligible to get COVID vaccine boosters, Israel is the first country to widely provide a third dose of a Western shot to residents.
"I intend to be the president of everyone," Herzog said after the votes were tallied.
Prime minister's Likud party continuing negotiations with far-right and ultra-Orthodox groups after winning March election.
Europe's nationalist parties are rushing to support formerly reviled Israel as an ally against the 'scourge' of Islamisation.
Benjamin Netanyahu's disavowal of the two-state solution could lead to a shift in U.S.-Israeli ties.
Turnout was high in the close contest between Isaac Herzog and Benjamin Netanyahu.
Netanyahu facing challenge to secure fourth term as he promises more settlements, no Palestinian state in final push
The Israeli election has exposed public fatigue with Benjamin Netanyahu's stress on national security rather than socio-economic problems.
Israeli PM stokes fears of centrist coalition with Arab backing as Zionist Union pulls ahead in polls
Israeli PM to deliver controversial address on Iranian nuclear programme to U.S. Congress.
An interview with a rising star of Israeli politics.