The four-year extension is a reward for his outstanding performances during the club's Premiership return over the last season.
Souness signed the Keeper from Liverpool on a free transfer during November of 2000. Brad is currently playing for the USA team in Japan. He will sign the new deal upon on his return.
"Brad has been an excellent player for us. We got him virtually on a free and he has been a great servant," said John Williams, Chief Exec at Rovers.
"We feel this new deal represents suitable reward and recognition for his achievements. It's good for him and it's good for the club."