The 28-year-old striker told the Sunday Times: "This is the hardest - and yet probably the most sensible - decision I have ever made.
"I am not a troublemaker and I do not kick up a stink if I am not in the team but enough is enough."
Jansen, who has made only one start for Rovers this season, says he will go on trial to earn a new deal at a new club.
He added: "I love the club but what was happening was tearing me apart.
"I have worked hard and put in some of my best training sessions but it is like I am invisible and no-one is watching.
"I respect manager Mark Hughes' decisions but I want to be playing."
Jansen moved to Rovers from Crystal Palace for £4.1m in January 1999.
He was tipped to win England honours until a motorcycle accident when on holiday in 2002 left him in a coma for four days.