The 28-year-old striker scored six goals in the Staggies’ Betfred Cup ties this season and will be looking to make an immediate impact under Hibs head coach Neil Lennon.
Graham told the club’s official website: “I am delighted to have joined Hibernian.
“I’ve been happy with my pre-season and start, and am looking forward to continuing this at Hibs.
“Everyone knows the size and stature of the club here. Promotion is the number one aim this season and I hope to be able to help achieve this.”
Lennon said: “We’re very pleased to have signed Brian.
“He’s a goalscorer and will give us another option going forward when we’re trying to break teams down.
“We’ve started the season well and the additions of Brian and Andy (Shinnie) will further strengthen our squad.”