Middlesbrough boss Gordon Strachan had already added to his squad in the transfer window with the signings of Barry Robson, Willo Flood and Chris Killen from Celtic, together with the loan additions of Stephen McManus and Kyle Naughton.
Australia international McDonald scored 50 goals in 88 league appearances for Celtic after joining the club in the summer of 2007.
Miller, meanwhile, has passed double figures for Aberdeen in the past two seasons and earned his second Scotland cap in November.
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