The 18-year stayed behind from Chelsea's pre-season tour in Japan to sort out a deal.
The Redbull-owned club are looking at offering the teenager regular football next season in Bundesliga and a chance in the Champions League.
Leipzig boss Julian Nagelsmann is looking to bolster his squad after qualifying for Europe's top competition.
And Ampadu can give him options at centre-back and defensive-midfield.
Ampadu, who joined Chelsea from English lower-tier side Exeter City, made just one senior appearance for the Blues last term.