Defender Elvedi made his Zurich debut as a 17-year-old last year and has also played 23 games for Switzerland's youth teams. He will sign his contract to 2019 straight after his medical, Gladbach said.
"Nico is a major talent who we think can make the leap to the Bundesliga," said Gladbach sports director Max Eberl.
"In the defence he can play as a central defender or on the right or he can even play in the central midfield and with 18 he is already experienced in professional football."
Gladbach finished third in the Bundesliga last season, reaching the Champions League group stage for the first time.
(Reporting by Karolos Grohmann; editing by Sudipto Ganguly)
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