The law was unanimously passed by the Knesset (parliament) after he backed the opposition's private members bill.
Education ministry figures show that 68 per cent of Jews and 5 per cent of Arabs attend kindergarten at age three, and 90 per cent of Jews and 8 per cent of Arabs at age four. Kindergarten is already obligatory and free from age five, while school starts at six. The new law is to be phased in over 10 years, from September, at an estimated cost of pound;140 m.
The right-wing Netanyahu toed the treasury's spending line until last month's vote to dissolve the Knesset. He took charge of the finance ministry after his Thatcherite minister resigned, and announced that it was "time to loosen the belt".
His U-turn received strong support from education minister Yitzhak Levy, whose National Religious party is worried that the rival Shas party is stealing pupils from its schools.
The NRP is linked with state religious schools, which educate some 20 per cent of Israeli Jews. State secular schools educate around 70 per cent, and independent, ultra-religious schools the rest. Independent schools are state-funded, and include those run by Shas.
Shas, launched 15 years ago, is already the third largest party in Israel, and polls predict it could double its strength in the May 17 elections. It appeals to poor Jews originating in Arab lands, offering strict religious observance as protection against secular ills.
Shas' growth owes much to its affiliated network of kindergartens and primaries, and to its ability to charge parents of three to five-year-olds up to 10 times less than rival organisations.But its teachers are generally less qualified.
Education is expected to play a bigger role than in past election campaigns. The opposition Labor party has been studying the campaign run by Britain's Tony Blair.
But the prospects for implementing the new free pre-school law will depend largely on the treasury, which remains implacably opposed.