The Lithuanian international joins the Dutch side on a permanent deal.
The 22-year-old joined the Reds in 2021, before heading to AFC Wimbledon on loan in January of last year until the end of the 21/22 campaign.
In September 2022, Kalinauskas joined Havant & Waterlooville on loan, returning to South Yorkshire in December.
The attacker made his debut for the senior Lithuanian national team on September 25 in a Nations League match against Luxembourg.
Everyone at Oakwell wishes Tomas well for the future.
