The decision of European football's governing body follows that of the world governing body last month to award the 2022 World Cup finals to Qatar.
England, Bulgaria, Wales and the Czech Republic were also bidding to stage the Under-21 tournament, UEFA's premier age-group competition.
The decision by the UEFA executive committee represented the second snub for England following their failure to win the right to stage the 2018 World Cup finals which FIFA awarded to Russia.
Israel previously hosted the European Under-16 tournament in 2000 and staged UEFA's annual Congress in Tel Aviv for the first time last year.
Israeli FA chairman Avi Luzon hailed the decision as an "unprecedented achievement" for the country.
"I am as excited and happy as I was when my first son was born, I hope that with this achievement Israeli football will receive a boost," said Luzon.
Israel had also been candidates to host this year's championships which will be held in Denmark.
As automatic qualifiers for the competition, Israel will participate in the event for the second time after playing in the 2007 championships in the Netherlands.
Israel originally played in the Asian Confederation (AFC) but were moved to Oceania because teams mainly from Arab countries refused to play them, before becoming full UEFA members in 1994.
The awarding of the event will add impetus to the building of new venues. Stadiums under construction in Haifa, Netanya and Petah Tikva are due to be ready in time and the 60-year-old National Stadium in Tel Aviv is also set for rebuilding.
There is also unlikely to be any debate about moving the tournament to the winter months as there is about Qatar's World Cup.
The hottest daytime temperatures in June and July would be around 30-35 celsius (86-90 Fahrenheit). While it will be humid along the coast, Jerusalem will be cooler and dry.
