The Serbia international has rejoined the Bundesliga club for the remainder of the season, having made just five appearances for Madrid in all competitions this term.
Jovic started only four LaLiga games in the previous campaign, having moved to Spain in a €60million transfer off the back of a hugely productive 2018-19 that saw him finish with 27 goals.
Eintracht are hopeful the 23-year-old can now "get back on track" in Germany, with the temporary switch suiting all parties involved.
"Luka didn't have an easy time in Madrid recently. It is important for him to get back on track. It was his great wish to return to Eintracht," said Eintracht sporting director Fredi Bobic.