Mr Verity, 56, was suspended in September when his assistant, Anne Ridley, made allegations about his behaviour which were eventually labelled "sexual" because his hand allegedly once brushed hers.
Mr Verity was cleared by governors of sexually harassing Ms Ridley, but had to resign because his position had become untenable. The row caused acrimony among staff, parents and governors.
Christopher Field, the acting head, was among applicants for the post, but some parents felt his appointment would be divisive, as he had been involved in the inquiry into the allegations against Mr Verity.
Mr Able, a former deputy head of Barnard Castle in Co Durham, graduated in natural sciences at Trinity College, Cambridge. He is married and has a son and daughter.