KBT has about 200MW of diesel and gas contracts on hire with Indonesian utility company PLN.
The deal will add to the 140MW that Aggreko already has contracted with PLN.
KBT has been serving the power rental market since 2010.
Aggreko chief executive Chris Weston said: "Aggreko has had a long and productive relationship with PLN and Indonesia, and this acquisition will deepen this further.
"PLN has been clear in its ambition to improve the power situation in East Indonesia in particular, and we will be well placed to support this with our extended presence and competitiveness."
Glasgow-based temporary power provider Aggreko has expanded its operations in Indonesia by acquiring power rental company KBT in a deal worth up to $32.8m (Â£25.7m).