The Swiss goalkeeper became the Hoops third signing of the summer on a free transfer following the loan deals of Daizen Maeda and Cameron Carter-Vickers becoming permanent.
Manager Ange Postecoglou had been keen to add to his goalkeeping options this summer and Siegrist will now challenge Joe Hart, who has been handed the No1 jersey following the exit of Greek flop Vasilis Barkas.
Frail is convinced the 30-year-old, who impressed during his four-year spell in Tayside, will serve it up to Hart and challenge for the position between the sticks.
The ex-Hoops coach is adamant Siegrist has what it takes to perform at the top level and believes he will help to drive standards among the goalkeeping department.
Speaking to the Scottish Sun, Frail admitted: “Benji’s a top keeper and a great boy. I’m delighted to see him join Celtic because of the person he is, and especially how hard he’s worked for this kind of fantastic opportunity.
“Benji will go there with the mentality he’s good enough to play for Celtic - and I think that’s precisely the attitude you need if you’re going to a club of that magnitude.
“He’s got the desire to play at the highest level possible. His target will be to get the jersey. He will push Joe Hart all the way to be No1.
“Hart is an excellent keeper with a tremendous pedigree and someone like Benji - a really good professional - could well push him to perform at an even greater level.
“That, of course, would only benefit Celtic, while there’s also another good keeper there in Scott Bain. Benji’s been in Scotland long enough. He’ll know the history and size of Celtic - and he’s still on 30.
“He won’t be satisfied with being a back-up goalie there, I’m sure that Siegrit will stake his claim to be first choice for Ange Postecoglou.
“For Dundee United, certainly the season I was there, Benji had a really good temperament. The job that Micky mellon did in keeping United in the Premiership was excellent - and a lot of that was down to the performances of Siegrist in goal.
“He’s a nice lad and totally focused on being the best he can be. Benji’s approachable, and from the first minute I started working with him I immediately realised he was a great team player. I really enjoyed coaching him at Tannadice.
“His professionalism was always evident. Benji’s demonstrated so many times he’s a brilliant shot-stopper but he does the basics very well while he’s a good athlete and has a big presence.
“Those types of keepers will always gain attention. It was no surprise to meCeltic were very keen to get a deal done. For a free transfer, it’s a no-brainer for me.
“Normally, someone of Benji’s calibre would cost a few million, so it’s great business for Celtic to secure his signing.”
Siegrist will work alongside well-renowned goalkeeping coach Stevie Woods going forward and his impressive track record of developing the likes of Artur Boruc, Fraser Forster and Craig Gordon will benefit the former Vaduz stopper hugely, according to Frail.
He added: “I know Stevie Woods well, a good man and a top coach. Benji will definitely benefit from his expertise.
“He was lucky also to work with Neil Alexander at Tannadice. he brought him on and Woods can be just as big an influence.”