Tight-head Rae, 22, has committed himself to the Warriors until May 2019, having joined in 2013.
Fellow Scot Bhatti, 23, has agreed professional terms with Glasgow for next season.
The loose-head has spent most of this season playing for Premiership side Melrose but has featured three times for the Warriors.
"It has always been a dream of mine to be a professional rugby player, so I'm really happy to have signed a contract with Glasgow," he told Glasgow's website.
Rae previously had spells on loan at London Scottish and Benetton Treviso and has been capped up to Scotland Under-20 level.
"Glasgow is my home club and all my family are here and I'm enjoying it," he said.
"I want to play well for my club and if I got the opportunity to play for Scotland one day, that would be a bonus."
Sixth in the Pro12, Glasgow visit third-placed Ospreys on Sunday.

Lieutenant Colonel Benedict Tomkins, 49, of Defence, Equipment and Support, based at Abbey Wood, near Bristol, is facing trial in the US.
He allegedly attacked the woman in her hotel room where he went under false pretences after a drinks reception.
The woman told the court Mr Tomkins was "very aggressive" and "took control".
The trial is being heard at Joint Base Andrews in Maryland. It is the first-ever court martial which will be held in the US and UK to allow more witnesses to testify.
The court heard that Mr Tomkins said he had had sexual activity with the woman, which "wasn't rose petals or cupid's arrows, it was fairly animal".
The incident is alleged to have happened after a dinner and a drinks reception at the Sheraton Hotel, Kampala, on 7 January 2015.
By the end of the evening, the young woman said she was "very drunk" when Mr Tomkins went to her hotel room.
"There was no talking, no romantic lead up to something that I recall. He did get much more aggressive and used some level of force to take things further," she said.
"The room was spinning, it was a very brief memory."
They later exchanged messages and he thanked her for a "wonderful evening" to which she agreed. She told investigators she initially feared reporting the incident in case it would harm her career.
The case is expected to resume in Bulford, Wiltshire, on Monday.

26 July 2016 Last updated at 17:48 BST
The company says its Dtek50 smartphone offers improved security over rival Android devices, and will cost less than its previous handset Priv.
It is the firm's second Android handset after switching focus away from its struggling BB10 platform.
One analyst said the phone was the "right move" but that the company still faced an "uphill battle" with devices.

The parade also commemorates Yeovilton's 75th birthday and is in recognition of the 70th anniversary of the end of World War Two.
Platoons from HMS Heron, led by the Queen's Colours and the Band of the Royal Marines, marched before Yeovil mayor Mike Lock.
There was also a flypast representing all the squadrons based at Yeovilton.
Lieutenant Commander Chris Gray said the freedom of Yeovil was granted to the base in 1962 and the parade "reinforces our bond and close links" with the town.
Props D'arcy Rae and Jamie Bhatti have signed new contracts with Glasgow Warriors.
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A married British Army officer denies raping a young female colleague at a UN event in Uganda, a court martial has heard.
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Blackberry has launched its first touchscreen-only Android handset, in a bid to diversify its range of devices.
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Royal Marines from RNAS Yeovilton have marched through Yeovil to mark the base's freedom of the town.