The 60-year-old will perform two songs at the event on 18 May, a popular hit and a new song, the European Broadcasting Union confirmed to Haaretz.
She is reported to have butted heads with Eurovision producers over the new track, said to contain political messages.
Madonna's performance at the contest is expected to cost around $1m (£765,000), which will be covered by billionaire businessman Sylvan Adams.
She will also reportedly be accompanied by a 160-person entourage.
Israel will host the popular singing competition after the country's 2018 entry, Netta, won with the song Toy.
It will be the fourth time Madonna has performed in Israel, having first played in 1993, followed by shows in 2009 and 2012.
Israeli Prime Minister Benjamin Netanyahu initially planned to hold the 2019 competition in Jerusalem, but tensions with Palestine forced the location change.
Last week, Mr Netanyahu announced it would cover 1.5m shekels (£314,896) of the security costs for the contest.
Reality show winner Michael Rice will represent the UK in the competition, who was picked during the BBC Eurovision You Decide 2019.
He will perform a track called Bigger Than Us.