Visser, who was born in Holland but qualifies for Scotland on residency grounds, has been the leading scorer in the Pro12 four campaigns running and has scored seven tries in 18 Test outings for his adopted country.
Quins won the Premiership just two years ago but currently lie eighth in the top flight and are on course to miss out on the play-offs for the first time since 2010-11.
“We are delighted to welcome Tim to the club,” said director of rugby O’Shea. “He is and always has been a finisher and, with the margins between winning and losing so small, players like Tim can be the difference. He is a great man, who is really driven to succeed.”
Visser moved north in 2009 after a spell at Newcastle but is looking forward to returning to the Premiership. “I am delighted to join a club with as much heritage as Harlequins,” said the 27-year-old. “It’s a dream come true and I’m looking forward to meeting my new team-mates and helping the club move forward.”