The 25-year-old only joined Boro in the summer in a £500,000 deal and was well favoured by Gareth Southgate.
But Strachan has not been a big fan of the winger and he said yesterday he was happy to let Yeates leave.
It is believed Boro have agreed a £500,000 fee with United, allowing more funds for Strachan to move for Queens Park Rangers' Wayne Routledge.