The New Zealander has penned a two-year deal with the Scottish side and will leave Connacht at the end of the current Magners League season.
Glasgow head coach Sean Lineen reckons Nathan fits the bill perfectly at Firhill stadium and will add some much needed experience to the youthful side.
"You can see the solidity and vision he has brought to the Connacht backline," said Lineen.
"He's a little bit older and with so many Scottish youngsters in our squad - which is good - and others hoping to be at the Rugby World Cup throughout September and October, we need an older head in the midfield. A bit of maturity and experience is what we need.
"He knows the game and has plenty Magners League experience. He's a top lad and is very ambitious so I know he'll make a difference."
The 27-year-old who is equally comfortable at fly-half or centre has been a mainstay in the Connacht side in recent years and has made 73 appearances for the province.
He will aim to go out with a bang when the Galway-based side finish their Magners League campaign at Munster on Friday.
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