The Danish stopper, who was a free agent, joins defender Josh Williams at Sandy Lane, who has also signed on dual registration from Gainsborough Trinity.
Budtz, 34, previously played at B 1909 and FC Nordsjaelland, before moving to England and signing for Doncaster Rovers, saving two penalties in a shoot-out with Manchester City on his debut.
He also counts Wolverhampton Wanderers, Hartlepool United, Oldham Athletic, Eastwood Town, Stalybridge Celtic and Buxton among his former clubs.
Mark Shaw moved to add Budtz after recent signing between the posts, Jon Stewart, broke a bone in his foot.
He said: “Jon wants to come back and play for the club, but we’ve been able to bring in a very experienced replacement in Jan.”
“He’s a good tall, commanding ‘keeper who played a key role in helping Gainsborough reach the FA Trophy semi-final last season”.
Shaw was keen to express his support for young keeper Ben Gathercole, who the manager revealed has been playing while injured for Tigers.
“Ben has come in for some criticism which I don’t think is as just as people believe, he’s been playing injured the whole time and he’s still got a big future ahead of him at the club,” said Shaw.
Williams meanwhile has signed on dual registration, and can play at centre-half or left-back, so would provide ideal cover for Phil Roe.
Shaw said: “I’m grateful to Steve Housham for letting us get Josh in, and we’re pleased to have another good, young player at the club to help add strength in depth.”
Worksop Town are at home to Stamford tomorrow in league action at Sandy Lane, at 3pm.