Middlesbrough will recoup the 500,000 they paid Colchester in the summer for the 25-year-old, who has made 17 appearances.
Sheffield United manager Kevin Blackwell confirmed after Saturday's victory over the Boro: "We have agreed a permanent deal and, hopefully, it will be completed on Monday. Gordon Strachan did not want him to go before we played each other."
Yeates could be the last arrival at the club during the January transfer window but Blackwell remains unsure if anyone will depart.
Defender Matt Kilgallon, whose contract runs out in the summer and who rejected a 1.5m move to Burnley last week and who did not make the Blades squad on Saturday due to a calf injury, continues to be linked with Everton but Blackwell says he would be delighted if he stays.
"We have been linked with everyone but there is very little transfer activity from anyone and I do not think I will be doing too much in any case," said Blackwell
"I don't know if Kilgallon will stay. There was an offer from Burnley that was accepted so you just don't know. In the last two transfer windows, I have lost James Beattie with a late deal and then Michael Tonge at 10.30pm on August 31 so you do not know what will happen."
Opposite number Strachan, who fielded three debutants from Celtic against the Blades, intends to use the money from the sale of Yeates to further strengthen and has been strongly linked with a move for Queens Park Rangers' Wayne Routledge.
Seven defeats in the 11 league games for which he has been in charge have seen the Boro fall to 13th and Strachan said: "The form is a concern. I don't just go home and whistle away and think life's great. Fortunately, I've been around 13 years doing this job. It wouldn't be great for a young manager to be in this position but as someone with experience I do know what has to be done and how to change it.
"It's not great, it's not nice and I wouldn't recommend it for anyone but you have to deal with it.
"I need to make us more whole, not bring in a whole new team. Instead of relying on one or two players, we need to be a whole team to get through games."