RB Leipzig will pay Roma an initial €4million loan fee for the 25-year-old, with the option to complete a permanent transfer next summer for a further €25million. The midfielder only joined AS Roma from RC Lens last year for around €23.5million, but struggled for consistent playing time in Serie A and leaves the Italian capital after a single season.
El Aynaoui said the move appealed both for footballing and personal reasons.
"RB Leipzig doesn't just have an outstanding reputation, the RBL playing style with high intensity, plenty of dynamism and the demand to want the ball ourselves suits me and my strengths very well," said El Aynaoui, the son of tennis legend Younes El Aynaoui.
"I'm really looking forward to RB Leipzig, the city and the sporting challenges in the Bundesliga, the Champions League and the DFB-Pokal."
Sporting executive Marcel Schäfer said the club had signed a player who fits their profile closely.
"With Neil El Aynaoui, we're getting a player who fits our profile and our playing philosophy very well," Schäfer said. "He brings tremendous running power and aggression, is very intense against the ball, and can simultaneously use his quality on the ball to provide dynamism and solutions in midfield. He is present on both sides of the ball and can cover large spaces."
El Aynaoui arrives with considerable international pedigree, having started every match for Morocco at both this year's Africa Cup of Nations and the World Cup, missing only seven minutes of action across the two tournaments.
He made 34 competitive appearances for Roma last season, scoring twice, and his market value is reported to have doubled over the course of the campaign despite his struggles for regular starts, underlining the level of talent Leipzig believe they have secured on loan.
Roma head coach Gian Piero Gasperini said the midfielder's participation at the Africa Cup of Nations, followed by the difficulties of readjusting on his return, had affected his form and opportunities in Serie A, with increased competition for places in midfield from Niccolò Pisilli, Bryan Cristante and Manu Koné making regular starts harder to come by.
The move gives El Aynaoui a fresh platform in Germany, joining a Leipzig side that has made an encouraging start to the season under new head coach Martín Demichelis.