He was educated at the free school, Norwich, whence he entered Corpus Christi College, Cambridge, as a scholar on Archbishop 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.
In 1680 he received the degree of D. D. , and was presented by Charles II to the important cure of St Martin's-in-the-Fields.
As vicar of St Andrew- the-Great, Cambridge, he was conspicuous for 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's Mancroft, Norwich.
In 1678, in a Discourse of Idolatry, he had endeavoured to fasten the practices of heathenish idolatry on the Church of Rome, and in a sermon which he published in 1681 on Discretion in Giving Alms was attacked by Andrew Pulton, head of the Jesuits in the Savoy.
A sermon which he preached on the commission was published the same year.
Tenison's reputation as an enemy of Romanism led the duke of Monmouth to send for him before his execution in 1685, when Bishops Ken and Turner refused to administer the Eucharist; but, although Tenison spoke to him in " a softer and less peremptory manner " than the two bishops, he was, like them, not satisfied with the sufficiency of Monmouth's penitence.
He preached a funeral sermon on Nell Gwyn (d. 1687) in which he represented her as truly penitent-a charitable judgment which did not meet with universal approval.
He attended Queen Mary during her last illness and preached her funeral sermon in Westminster Abbey.
He crowned Queen Anne, but during her reign was not in much favour at court.
A strong supporter of the Hanoverian succession, he was one of the three officers of state to whom on the death of Anne was entrusted the duty of appointing a regent till the arrival of George I, whom he crowned on the 316t of October 1714.
Besides the sermons and tracts above mentioned, and various others on the " Popish " controversy, Tenison was the author of The Creed pf Mr Hobbes Examined (1670) and Baconia.
As archbishop, he was close to William III and crowned Anne and George I, but, as a leading advocate of the Hanoverian succession, he was isolated by extreme Tories.
He successfully steered the church through the convocation controversy, though convocation itself was abandoned.
Gibson wrote of his ‘great goodness and integrity’ and ‘natural sedateness’ which preserved the church from shipwreck in stormy times.
Being a strenuous opponent of the Church of Rome, and Whitehall lying within that parish, he stood as in the front of the battle all King James's reign.
He showed compassion for the poor, and promoted voluntary societies and charity schools, the foundation of the Society for Promoting Christian Knowledge and the Society for the Propagation of the Gospel, and the demand for bishops in America.
In appearance he was described as a large, brawny, "hulking" figure, very strong when young but afflicted with gout in later life.
He married Anne, daughter of Richard Love; but died without issue. Edward Tenison (1673–1735) LL. B (Cantab. ), his cousin, became Bishop of Ossory (Ireland) (1730/1731-1735). Another relative, Richard Tennison (1642-1705), became Bishop of Meath. Thomas is said to have advanced Richard in his career: in his will he left legacies to all of Richard's five sons.