Dual-listed sleep device manufacturer ResMed has completed the $US225 million ($A306 million) purchase of Wisconsin-based asthma and pulmonary specialist, Propeller Health.

ResMed, listed in both the US and on the ASX, said on Monday it will allow Propellor to operate as a stand alone business as part of its new parent's Respiratory Care portfolio.

Propeller's digital medicine platform consists of small sensors that attach to consumers' asthma inhaler and pair with a mobile app to automatically track medication use and provide feedback and insights.

ResMed shares were last trading at $15.39 on the ASX, up 37 per cent from $11.15 a year ago.

The company paid $US750 million for health software provider MatrixCare in November