Chymee, Wikipedia agrees with Joseph. The tune originated with chassidim, the song, at Hebrew U.
According to an online article, Avraham Zvi Idelsohn, …a passionate Zionist … sought to pioneer a new style of modern national music that would unify the Jewish people as they returned to their historic homeland in Palestine. To that end, he arranged and composed many new Hebrew-language songs based on traditional melodies. These modern songs with ancient roots quickly became popular as new Hebrew folk songs, sung in kibbutzim, moshavs and printed in songbooks in the Jewish community of pre-state Israel and beyond. Among them was Hava Nagila.