The winger will officially join Saints on Saturday 3rd January, initially on loan until the end of the season with a view to a permanent transfer next summer.
Holland international Elia moves from German Bundesliga side Werder Bremen, having previously played in Italy and his homeland.
The 27 year-old began his career with ADO Den Haag before moving to FC Twente. He then joined Hamburger SV in Germany and spent a brief spell with Juventus before signing for Bremen in 2012.
Elia has 28 caps for his country, and played at the 2010 FIFA World Cup finals.