Sir Thomas Green came from a family that had been settled in Northamptonshire for at least a hundred years before his birth. His mother's family, the Throckmortons, originally from Worcestershire, had risen to prominence when her father, a client of the Beauchamp Earls of Warwick, became Under-Treasurer of the Exchequer. Sir Thomas does not appear to have played any prominent part in public life. He married Joan Fogge, in the late 1480s and the couple had two daughters.
It is unknown whether Sir Thomas participated in the Wars of the Roses. Like many families, his loyalty may have been torn as his mother's family were Lancastrian, whilst his wife's was Yorkist. The only glimpse of his political affiliations is in the charge of treason against him made in 1506. He was sent to the Tower of London, accused of taking part in treasonable activity by the Yorkist heir, Edmund de La Pole. Sir Thomas apparently was cleared of the charge, but died before he could be released from prison, leaving a considerable estate to his two daughters.