The Rangers, struggling to nail down an Eastern Conference playoff spot as Wednesday's NHL trading deadline neared, obtained the left wing in exchange for two 2013 draft choices and a conditional second-round choice in 2014.
Clowe -- who two years ago set career highs of 24 goals and 62 points -- had to waive his no-trade clause in order to make the deal happen.
Since then however, the 30-year-old Canadian's production has dropped off. This season he has compiled just one goal and 11 assists over 28 games.
"Ryane is a tremendously respected player and teammate, and an individual of outstanding character," Sharks General Manager Doug Wilson said.
"These deals involving players who have spent a substantial amount of time in and contributed much to San Jose are difficult, but it's also important for us to get value for a player who is set to be an unrestricted free agent."
Clowe has amassed 101 goals and 271 points with 567 penalty minutes in 423 NHL appearances since 2005, all with San Jose.