He was born at Cottenham, Cambridgeshire, the son and grandson of Anglican clergymen, who were both named John Tenison; his mother was Mercy Dowsing. He was educated at Norwich School, going on to Corpus Christi College, Cambridge, as a scholar on Archbishop Matthew Parker's foundation. He graduated in 1657, and was chosen fellow in 1659. For a short time he studied medicine, but in 1659 was privately ordained. As curate of St Andrew the Great, Cambridge from 1662, he set an example by his devoted attention to the sufferers from the plague. In 1667 he was presented to the living of Holywell-cum-Needingworth, Huntingdonshire, by the Earl of Manchester, to whose son he had been tutor, and in 1670 to that of St Peter Mancroft, Norwich.