http://news.bbc.co.uk/sport1/hi/football/teams/m/middlesbrough/8447259.stmCeltic quartet Barry Robson, Gary Caldwell, Willo Flood and Chris Killen are having medicals in Middlesbrough ahead of moves to Teesside.
An offer was accepted last week for Caldwell and Robson and a deal for the other two has now been agreed.
Caldwell will sign for three and a half years and Robson for two and a half.
It had been thought that Flood and Killen would move on loan, but Middlesbrough will now take over the remainder of their Celtic contracts.
It means Flood will be tied to the Coca-Cola Championship club for 18 months, while Killen's deal lasts until the summer.
Middlesbrough hope to conclude the deals on Tuesday should the medicals prove successful.
Strachan, who signed all four players while manager of Celtic, has spoken of the need to bring "leaders" into his squad during the current transfer window.
Defender Caldwell, who is out of contract at Celtic Park in the summer, has also been the subject of interest from Barclays Premier League club Wigan Athletic.
Irish midfielder Flood and New Zealand striker Killen are not in the first-team picture with the Scottish Premier League club.
During his tenure at Celtic, Strachan signed Caldwell under freedom of contract from Hibernian in 2006 and took Killen from the same side the following year.
Robson was captain of Dundee United when he moved to SPL rivals Celtic in January 2008 for £1m.
Meanwhile, fellow Tannadice midfielder Flood, on loan from Cardiff at the time, followed suit last January for a fee of about £200,000.
