The 22-year-old was out of contract this summer and with first-team opportunities limited, has moved to secure his longer-term future.
AIK have paid an undisclosed fee for the striker, who will link up with former Black Cat midfielder Seb Larsson.
Sporting Director Kristjaan Speakman said the youngster would be missed at the club but added that the switch 'was a good opportunity'.
“Benji has been unable to make an impact at first-team level due to incredibly strong competition for places and understandably he has a desire to play regular senior football, so this represents a good opportunity for him," Speakman said.
"He’s a likeable young player who will be missed by his team-mates and club staff, but we wish him the very best in the next chapter of his career."
Kimpioka has made just four senior appearances this season, but did score in the 5-0 win over Sheffield Wednesday just before the turn of the year.
Kimpioka moved to Wearside in July 2016 and made 16 first-team appearances in all competitions, scoring on four occasions.
The forward featured more than 50 times for the club's U23s, whilst also spending time on loan with Torquay United and Southend United in 2021.
The move further depletes the club's striking resources, following Jermain Defoe's retirement last week.
Alex Neil's options were strengthened this week when Nathan Broadhead returned to training as he seeks to get back to full fitness following hamstring problems.