The Netherlands international spent the second half of last season at Southampton and will now continue his career back in his homeland
The Dutch winger spent the second half of last season on loan at Southampton, making 17 appearances for the Premier League side, and had previously expressed a desire to remain at St Mary's Stadium on a permanent basis.
However, he will now return to the Eredivisie for the first time since leaving Twente in 2009.
Elia has signed a two-year deal at Feyenoord, whose technical director Martin van Geel stated: "With his experience and his qualities he can definitely help our team. We are very happy that Eljero has chosen Feyenoord.
"He has played over the years at big clubs in major European leagues."
Elia joined Bremen from Juventus in 2012, having previously spent two years in the Bundesliga with Hamburg.
He boasts 28 caps for the Netherlands, but has not represented his country since 2012