Jansson joined Torino from Malmo in 2014, but has since made only 16 appearances in Serie A.
The 25-year-old has won eight caps for Sweden and was an unused member of their Euro 2016 squad.
"I need to play football regularly and I know that Leeds are a big club with big ambitions," he said.
"I want to help take Leeds back to the Premier League as soon as possible. I'm an aggressive defender and I always give more than 100% for the team that I play for."