Al Habsi, who has agreed a three-and-a-half-year contract, will arrive at the Reebok Stadium once the relevant paperwork has been completed.
A club spokesman said: "He will join up with the squad once his work permit has come through."
Al Habsi, who is rated as one of the top goalkeepers in Asia, was due to move to Bolton after the end of the Norwegian season in October.
Meanwhile, Bolton Wanderers and Everton are being linked with Blackburn Rovers striker Matt Jansen.
Jansen is ready to leave Ewood Park this month in search of first team football and is meeting with manager Mark Hughes before the weekend to discuss his plans.
The Daily Mail says Bolton and Everton have stepped in and are heading a queue of clubs seeking talks with the striker.