Bristol City were reported to have made an offer earlier this month, while Crystal Palace and Sheffield United were also keen.
However, Boro are understood to have agreed a fee in the region of £500,000 with Colchester and have persuaded Yeates to head to the North East.
Yeates - who can play on either flank - joined Colchester on a permanent basis from Tottenham Hotspur two years ago, but he has just 12 months remaining on his contract.
He has scored 21 goals in 81 appearances for the League One club, having previously spent the 2005/06 season on loan with the Us.