Bern says it has signed Streit and Geneva-Servette says it recruited Weber.
Geneva-Servette coach Chris McSorley says the club expects to announce another signing on Wednesday.
San Jose Sharks captain Joe Thornton is also expected in Switzerland this week after saying he would rejoin Davos.
Thornton played with the Alpine town team during the 2004-05 NHL lockout season, alongside New York Rangers winger Rick Nash. Nash is also being pursued by Davos.
The NHL formally locked out its players on Sunday after the collective bargaining agreement expired.
The 12-team Swiss top division began its season last week.