The 21-year-old, who joined the Major League Soccer club on a trial in June, will be added to the roster when he receives his international transfer certificate, the Impact announced Wednesday.
''Dennis is a very good left-sided player who we think will establish himself in MLS after some strong years in Switzerland,'' Impact head coach Jesse Marsch said in a statement. ''He did his training at FC Basel, which is a club that is renowned for developing great players.''
The five-foot-10 Iapichino was a teammate of the Impact midfielder Felipe Martins with Lugano in the Swiss league.
He spent his developing years with Basel and was loaned to second division squad Biel during the 2009-10 season. He was then loaned to FC Lugano, where he played 25 league matches and two Swiss Cup games.
He joined Lugano full-time in 2011-12.
Iapichino also played six friendly games with the Swiss under-20 national team.
He will count as an international player on the Impact roster.
''We're very happy and excited to add a young player like Dennis to our roster,'' said Impact sporting director Nick De Santis. ''At his age, he's already played a lot of professional games at a high level and we feel that he can settle right away in MLS like Felipe, Andrew Wenger and Zarek Valentin.
''It's tough to find left sided players and his technique and abilities are very good.''
The Impact have Jeb Brovsky playing left back, backed up by Tyson Wahl and Josh Gardner.
The club also announced it traded little-used forward Justin Braun to Real Salt Lake for a conditional pick in the 2014 MLS SuperDraft. Braun had one assist in five games in Montreal. He was acquired Nov. 23 in a trade with Chivas USA.
On Tuesday, the team loaned midfielder Bryan Arguez to Edmonton of the NASL.