Flood's deal extends to June 2011 while Killen's runs until the end of the current season.
The three men, who all played for the Bhoys under Strachan, passed medicals on Teesside earlier this week.
However, central defender Gary Caldwell, who was part of the original package, has joined Wigan instead.
The successful completion of the deals will come as a boost to Strachan, who will hope to be able to include his new recruits in the squad for Saturday's Championship clash with Sheffield United.
Boro currently lie in 11th place in the table, 14 points adrift of an automatic promotion place.
They have not given up hope of reeling in top two Newcastle and Nottingham Forest, although they realise their best chance of making a swift return to the top flight could be via the play-offs.
Strachan's side have won just two of the 11 games they have played since he took over from Gareth Southgate and need a major improvement if they are to climb the table during the remaining months of the campaign.
Midfielder Robson, 31, who won his seventh senior cap for Scotland in November, has a league title to his name and played Champions League football during his two years at Parkhead.
Republic of Ireland Under-21 international Flood, now 24, began his career at Manchester City and joined Celtic 12 months ago after two seasons on loan at Dundee United, while 28-year-old former City and Oldham striker Killen is a New Zealand international.
Their arrivals came as Boro confirmed that Egypt midfielder Mohamed Shawky has joined Turkish club Kayserispor on a free transfer.