Buddies boss Alan Stubbs admitted earlier on Friday that a deal for the 25-year-old was dead, as they welcomed the arrival of Nicolai Brock-Madsen from Birmingham City.
He told the broadcast media: “We were hopeful of getting the signing of Stefano across the line. Unfortunately, over the last day, that won’t be happening anymore. It’s disappointing but that’s transfer business.”
Stubbs had been confident of bringing both players to the Ladbrokes Premiership new boys earlier in the week.
A package had been agreed with Juventus which would have seen the player move on a season-long loan.
Beltrame, who had initially agreed to move to Paisley, then had a change of heart, preferring instead to return to the Netherlands with second tier, where he is likely to complete a move to Den Bosch.
The Italian previously spent time on loan with the southern Netherlands club in the 2016/17 season. He also performed in the Eerste Divisie last term with Go Ahead Eagles.
Meanwhile, loan signing Brock-Madsen revealed how former Dundee and Aberdeen attacker Greg Stewart sold him on a move to the Ladbrokes Premiership.
He said: “Greg was one of the first guys I talked with about coming here. He was up here at Aberdeen last year and has a really good knowledge about how the league is and what’s going on.
“I got some really positive feedback from him which really helped my decision.
“It was good to talk to him and then when I talked to Alan I was like, ‘Yeah this is what I want to do now’.
“I don’t know what Greg’s plans are but I told him I’d be really happy if he came here too. He needs to do what’s right for him though so we will see what happens.”