Strome, a fifth-overall pick of the New York Islanders in 2011, had a goal and an assist in 18 games with Edmonton this season. He has 59 goals and 103 assists in 358 career NHL games with the Islanders and Oilers.
Spooner had a goal and an assist in 16 games this season with the Rangers. He has 46 goals and 114 assists in 289 games with the Boston Bruins and Rangers.
Spooner was acquired from the Bruins in the trade-deadline deal last season that sent Rick Nash to Boston. He showed promise and was signed to a two-year, $8 million deal in July.
But Spooner has not been a good fit for the new system used by head coach David Quinn and has seen reduced playing time.
"With Ryan Spooner kind of being the odd man out on our team, and the opportunity to get somebody that we like his versatility," Rangers general manager Jeff Gorton said. "[Strome] can play center, he can kill penalties -- just a different kind of player that I think we can put in our group, and it's going to hopefully be a better fit for us."