The 26-year-old then spent a loan spell at AFC Wimbledon where he suffered a serious knee injury.
On his Twitter account, Elder said: "It's been emotional. It's been a tough year but what will be will be."
He continued: "Sad to leave a great set players and some unbelievable fans. Good luck to shrews in the future."
The former Brighton forward scored two goals during his 19 league appearances for the Shrews.
Elder has been linked with a possible return to AFC Wimbledon, who will play in League Two next season after achieving promotion from Blue Square Bet Premier.
Source: BBC Sport
Source: BBC Sport