The 22-year-old will be able to make his debut for the League One side on Saturday if he receives Football League clearance in time.
The Hornets paid IFK Gothenburg £3m for Dahlberg three years ago but he is yet to play for them, instead sent out on loans with IFK Gothenburg and Emmen.
Rovers manager Richie Wellens had been looking for a goalkeeper who would provide genuine competition for Louis Jones without tying the club into punishing financial penalties if the loanee was not selected.
Dahlberg has two senior caps for Sweden, having also played for them at under-21 level.
Doncaster have been heavily dependent on loanee goalkeepers in recent years, with Ellery Balcombe, Joe Lumley, Joe Bursik and Seny DIeng borrowed over the last two seasons.
Rovers begin their League One campaign at home to Wimbledon on Saturday.