The 26-year-old centre-back, who represented his country at Under-23 level, was a free agent after leaving Norwegian side Tromso this summer.
Fojut started his career in England with Bolton Wanderers, from where he had spells on loan with Stockport County and Luton Town before heading home to play for Slask Wroclaw.
He was linked with a move to Celtic before joining Tromso in December 2012.
Fojut told the club's website: "I played in English football for five years and it was always my wish to play in the United Kingdom once more. This is a great club and I feel this will be an excellent move for me and my career.
"I look forward to helping United continue the progression it has shown over the last few years and I would like to win trophies for the fans."
Boss Jackie McNamara added: "Jarosław is a strong and aggressive player. He will add to our defence and I am delighted to have secured him.
"We now have strong competition in the central defensive area of our squad and that was something we knew we had to address this pre-season.
"He is a commanding player who knows British football from his time at Bolton and he will fit in well at Tannadice."