The school, funded by the Drapers' Company, opened 138 years ago. It is one of only four schools in Wales where 100 per cent of GCSE pupils achieved five or more grade A to C passes last year.
More than 200 pupils and more than 80 teaching and domestic staff are affected. Fees are currently Pounds 3,282 a term for boarders.
Alistair Lang, clerk to the Drapers' Company, said this week: "The school has been trading at a loss for some time. It is working closely with other schools in order to assist parents with alternative placement from next September. "
Howell's is the third independent school in Wales to close in the past few years. The others were Lindisfarne College near Wrexham and the Indefatigable School, Anglesey.