The Bundesliga club will pay a fee of €3.5 million, with a further €500,000 depending on certain performance-related conditions being met.
If Leipzig qualify for the 2020-21 Champions League, they will have the option to make Shick's transfer permanent for €29m (£26.4m/$31.8m).
"Of course, I came here to help the team and achieve our goals together. I am glad that everything worked out in the end with RB Leipzig."
A youth product from Sparta Prague, Shick had seen a proposed move to Juventus collapse despite undergoing a medical in Turin – a saga that seemingly lingered over an underwhelming start to life in Italy's capital.
His move was eventually made permanent for a reported €37 million (£33.7/$40.6m) in June 2018 but life did not improve for Schick as he continued to struggle to meet the heights he reached in his first season in the Italian top-flight.
Over the course of 57 appearances for Roma in all competitions, he managed eight goals and will now look for a new lease of life with Julian Nagelsmann's Bundesliga pacesetters.
Leipzig are the only team in Germany's top flight with a 100 per cent record from their opening three matches and host Bayern Munich in a mouth-watering clash on their return to action following the international break.
Roma have bolstered their attacking options on transfer deadline day with the loan signing of Nikola Kalinic from Atletico Madrid, with Henrikh Mkhitaryan also completing a switch from Arsenal.