Siegrist, a Switzerland Under-21 international, will go straight into the Albion squad for the Sky Bet League Two fixture against Plymouth at Home Park on Saturday.
He has been brought in by manager Gary Rowett after Sunderland recalled Jordan Pickford.
"We've been watching Benji for some time now - (goalkeeping coach) Kevin Poole, (assistant manager) Kevin Summerfield and I have all watched him and have been impressed," said Rowett.
"We're always interested in strengthening our squad and at 6ft 4in he's a big goalkeeper and has some good attributes.
"We now have two excellent young goalkeepers who are both there to challenge each other and will both be looking to start matches."
Siegrist was part of the Switzerland squad at the London 2012 Olympics.
He is yet to make a senior appearance for Villa but is highly thought of by the Barclays Premier League club.