Berget has signed a deal with the Scottish champions until January, with Ronny Deila's side retaining an option to buy the attacker in the New Year.
The Norway international was brought to Cardiff in January this year by Ole Gunnar Solskjaer, who had managed him at Molde, and will link up with another countryman in the shape of Deila, his former boss at Stromsgodset during a loan spell.
Berget is eligible to make his Celtic bow in Wednesday's UEFA Champions League third qualifying round first-leg clash with Legia Warsaw.
He told Celtic's official website: "I am delighted to join Celtic and I'm looking to make the very best of this great opportunity.
"I know what a magnificent club Celtic is and what the club means to the supporters - it is a real privilege to be here.
"I also know the manager very well and I am delighted to be teaming up with him again and, of course, the great squad of players at the club."
Heading out the exit door at Parkhead is Watt, who has signed a five-year deal with Belgian Pro League runners-up Standard.
Watt's finest hour with the Glasgow club came in November 2012 as his strike secured a memorable 2-1 Champions League group-stage triumph over Barcelona.
However, the 20-year-old failed to live up to that lofty billing and spent last season on loan with Standard's domestic rivals Lierse, scoring nine goals in 18 outings.