Rabbi Dweck, who previously headed a Jewish day school in New York, will help shape the ethos of the new school.
Backers of the NJHS intend to submit a bid for a new school to open in north Barnet or south Hertfordshire in 2018 as soon as the government announces the date for the next round of applications for free schools.
While its ethos will be Orthodox, it will have an inclusive outlook, they said.
The NJHS project was formed out of the merger of the teams previously behind the separate Barkai and Kavanah College free school bids, which were turned down by the Department for Education in December. Kavanah had been backed by the United Synagogue and the Chief Rabbi.
The Chief Rabbi, however, now favours the expansion of existing Jewish schools to cater for rising demand rather than create a new school.
