Michael Spindelegger says they will now work to overcome remaining practical hurdles to finalise the legislation by the end of this year.
The group including Germany, France and Italy is set to inform the 17 EU countries not participating at a finance ministers' meeting in Brussels today of the decision.
European officials started pushing for the tax following the 2008-09 financial crisis to curb speculation and claw back revenues after government bailouts of banks.
The levy's scope won't be as broad as supporters initially hoped, focusing on taxing stock and derivatives trading.