Hibs are awaiting international clearance which would make the keeper available for Sunday's Edinburgh derby.
Smith, who began his career at Rangers, spent four years at Fir Park before joining Brighton in the summer on a two-year deal.
He told Hibs' official website: "I am delighted to be joining Hibernian.
"Everything about the club is exciting at the moment, from the gaffer, the training facilities to the results and team on the park.
"I want to be part of it, and will be working as hard as I can to get into the team on a regular basis."
Manager John Hughes said: "Graeme is an experienced SPL keeper and provides us with another excellent option in goal.
"I want competition for all positions at this club and Graeme has the right character and skills to play a key part in helping us build success for Hibernian."
Smith's signing is bound to raise question marks over the long-term future of Yves Ma-Kalambay, who is out of contract in the summer.
The last transfer window saw Hughes sign Graham Stack, who had been Hibs' number one until being struck down by a back injury which he is expected to recover from in time for Sunday's SPL clash with Hearts.