A successful spell at Tynecastle led to a £225,000 move to Dundee United in 2005, but he moved for free a year later to the Dons, for whom he signed a two-year contract extension in May 2008.
Strachan had already returned to his former club to sign four players during the current transfer window before securing McDonald.
Striker Chris Killen and midfielders Barry Robson and Willo Flood have all moved to Boro on permanent deals and defender Stephen McManus has joined them on loan.
Now McManus and Robson have been followed by Scotland team-mate Miller.
Meanwhile, Aberdeen have compensated for the loss of Miller by signing Steven MacLean on loan from Plymouth Argyle.
Hearts had also been interested in MacLean, but the player had been holding out for a permanent transfer.
Dons manager Mark McGhee is also hopeful of signing on loan MacLean's Plymouth team-mate, Jim Paterson, the left-back who played for the Dons boss at Motherwell.
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