Brommapojkarna are buying out the 32-year-old, who joined Malmö in 2023 from Djurgården.
There, Berg was reunited with coach Henrik Rydström, with whom he had spent time at Kalmar FF.
The Norwegian has also previously represented GIF Sundsvall.
"There have been both tough and very nice moments, and I leave with friendships with many nice people from my time in Malmö," says Berg in a statement on the MFF website.
Berg accounted for three goals and eight assists in 67 games in the sky blue jersey. He leaves Skåne with two Swedish championship gold medals and a cup title on his CV.
