Graham replaces Blade Thomson for the matches against South Africa on Saturday and Argentina the following weekend, and will hope for a first taste of senior international rugby having come close with England.
The 26-year-old plays for Newcastle Falcons and qualified for Eddie Jones's side on residency grounds, but says his heart has always been with Scotland and he made that clear to coach Gregor Townsend.
"I'm Scottish through-and-through but England asked me first as I'm eligible through residency. It would have been a silly opportunity to pass up, as I hadn't been selected for a Scotland squad since U20s," Graham was quoted as saying by Scottish Rugby on Monday.
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"I'm absolutely delighted to get this opportunity. I phoned Gregor to assure him I wanted to play for Scotland, and always wanted to play for my country. It's where I'm from and where I played most of my rugby."
Townsend says the flank, the son of former Scotland international prop George Graham, has been on their radar for some time.
"It was great to hear from Gary that he wanted to commit to Scotland. It has become a competitive environment for dual-qualified players recently and we know that these are not easy decisions for players," he said.
"We've been tracking Gary since he was at Jersey (Reds) and his form over the past 12 months at Newcastle has moved him closer to playing international rugby."
Scotland opened their November internationals with a 21-10 loss to Wales in Cardiff, but bounced back with an emphatic 54-17 victory against Fiji at Murrayfield on Saturday.
(Reporting By Nick Said; Editing by Christian Radnedge)
