The cheapest way I know is to get a bus from Nazareth all the way to Amman using a company called Nazarene Tours. The bus departs almost daily at 8AM and will cost around $20. You will be dropped off around Amman University. A public bus from Tel Aviv to Nazareth will cost you less than $10.
Another company called Mazada Tours has a direct bus from Tel Aviv but the cost is around $90. Not worth it.
If you don’t want to take a private bus for some odd reason, you can take a public bus to Bet She’an (around $15), a taxi to the border ($15), then a taxi from the border to Amman ($55+).
If you are not traveling alone you can use a Taxi, which could run you by my calculation about $250pp.
If you want it even cheaper you can do a more complicated route of Tel Aviv – Eilat (#393, #394), Eilat – Aqaba and finally Aqaba – Amman.
Or you can do a straight trip as described on True Nomads, which would all run a lot less then $400 for a flight.
Credit:stackoverflow.com‘