The Ohio outfit have brought in the 25-year old midfielder and the selection in exchange for the Crew's Second Round 2014 MLS SuperDraft selection and allocation money.
"Hector is an exciting young player and we are pleased to welcome him to our club," said Crew head coach Gregg Berhalter.
"He is a player that possesses several strong attacking attributes and will help our squad immediately."
Jimenez spent three seasons with the Galaxy, appearing 43 times for four goals and six assists.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball